Field Approximation Research Articles

On the optimal approximation of geophysical fields

On the optimal approximation of geophysical fields

Momentum dependent mean-fields of hyperons & antihyperons

The in-medium properties of hyperons and antihyperons are studied with the Non-Linear Derivative (NLD) model and focus is made on the momentum dependence of strangeness optical potentials. The NLD model is based on the Relativistic Mean Field (RMF) approximation to Relativistic Hadrodynamics (RHD) approach of nuclear systems, but it incorporates an explicit momentum dependence of mean-fields. The extension of the NLD model to the baryon and antibaryon octet is based on SU(6) and G-parity arguments. It is demonstrated that with a proper choice of momentum cut-offs, the Λ and Σ optical potentials are consistent with recent studies of the chiral effective field theory(χ -EFT) and optical potentials are consistent with Lattice-QCD calculations, over a wide momentum region. We also present NLD predictions for the in-medium momentum dependence of ∧¯, ∑¯ and Ξ¯ hyperons. This work is important for future experimental studies, like CBM, PANDA at FAIR and is relevant to nuclear astrophysics as well.

Improved Hybrid Algorithm for Composite Scattering From Multiple 3D Objects Above a 2D Random Dielectric Rough Surface

In this paper, an improved hybrid scheme combining the method of moment (MoM) and physical optic (PO) is proposed to analyze composite scattering from multiple 3D conductingobjects above a 2D random rough dielectric surface. In the calculation scheme, rough surface scattering is calculated using the PO method and target scattering is calculated by the MoM. The coupling interactions between the multiple targets are considered using the domain distribution method (DDM), where the matrix equations are constructed upon each individual target and are then presented and solved as a whole. The contribution from rough surface scattering, which is calculated by the PO method, is coupled with the impedance matrix, and the unknowns must be considered only in the MoM region. Most of the composite scattering problems are computing interactions between objects and rough surface, and solving the complex impedance matrix equation in the MoM part. To solve these two problems, first, the combined multilevel fast multipole algorithm (MLFMA) and the fast far field approximation (FaFFA) are introduced to accelerate interactions between objects and rough surface, where the near area on the rough surface is computed by MLFMA, while the far area is computed by FaFFA. In addition, to further improve the efficiency, the adaptive integral method (AIM) is employed to solve the impedance matrix equation of the MoM part in the scheme. The results are compared to those obtained with the traditional MoM-PO method, showing that the hybrid method proposed in this paper can maintain a high accuracy with a much smaller computational time and fewer resource requirements. The numerical results obtained under several different conditions are presented and discussed in this paper.

A C^1-continuous Trace-Finite-Cell-Method for linear thin shell analysis on implicitly defined surfaces

A Trace-Finite-Cell-Method for the numerical analysis of thin shells is presented combining concepts of the TraceFEM and the Finite-Cell-Method. As an underlying shell model we use the Koiter model, which we re-derive in strong form based on first principles of continuum mechanics by recasting well-known relations formulated in local coordinates to a formulation independent of a parametrization. The field approximation is constructed by restricting shape functions defined on a structured background grid on the shell surface. As shape functions we use on a background grid the tensor product of cubic splines. This yields C^1-continuous approximation spaces, which are required by the governing equations of fourth order. The parametrization-free formulation allows a natural implementation of the proposed method and manufactured solutions on arbitrary geometries for code verification. Thus, the implementation is verified by a convergence analysis where the error is computed with an exact manufactured solution. Furthermore, benchmark tests are investigated.

A Thermodynamically Consistent Formulation for Dynamic Response of Thermoviscoelastic Plate/Shell Based on Classical Continuum Mechanics (CCM)

This paper presents a thermodynamically consistent and kinematic assumption free formulation for dynamics of thermoviscoelastic plates/shells based on the conservation and balance laws of classical continuum mechanics (CCM) in which dissipation mechanism has been incorporated through ordered rate constitutive theory for deviatoric stress tensor. In this paper, we consider small deformation, small strain. The conservation and balance laws of CCM in [Formula: see text] in Lagrangian description using Cauchy stress tensor ([Formula: see text]) and linearized Green strain tensor ([Formula: see text]) constitute the mathematical model. The constitutive theory for the deviatoric Cauchy stress ([Formula: see text]) is derived using conjugate pairs in entropy inequality in conjunction with representation theorem. The argument tensors of [Formula: see text] are [Formula: see text] and rates of [Formula: see text] up to order [Formula: see text]. This yields a constitutive theory with dissipation mechanism based on rates of strain up to order [Formula: see text]. Constitutive theory for heat vector is also derived using the conjugate pairs in the entropy inequality and representation theorem. Finite element method is used to obtain solutions of the initial value problems descried by the balance of linear momenta (BLM), energy equation and the constitutive theories. The shell element geometry is described by the middle surface and the nodal vectors at the middle surface defining bottom and top surfaces of the element. The local approximation for the displacement field is [Formula: see text] - version hierarchical in the plane of the element as well as in the transverse direction. A space-time decoupled finite element formulation using Galerkin Method with Weak Form (GM/WF) in space is constructed for BLM as well as energy equation, both resulting in ordinary differential equations (ODEs) in time. The ordinary differential equations (ODEs) in time resulting from the finite element formulation of BLM are used to study: (i) natural undamped modes of vibration (ii) the transient dynamic response using the ODEs in time recast in modal basis: (a) using Rayleigh damping (b) using the ordered rate damping proposed in this paper. Time response is calculated using modal damping based on Rayleigh damping as well as using the proposed ordered rate damping mechanism. Model problem studies are presented to demonstrate: (1) accuracy of the natural frequencies obtained from the present formulation for thin and thick plates/shells (in which shear deformation is significant) and the results are compared with the currently used plate formulations (2) accuracy of damped transient response using proposed damping mechanism is compared with time response using Rayleigh damping (3) it is shown that Rayleigh damping has no physical basis and leads to spurious stationary states. The proposed damping yields accurate stationary states that are in exact agreement with the solution of corresponding BVP. A single formulation presented in this paper remains valid and accurate for very thin as well as very thick plates/shells and correctly simulates 3D state of deformation regardless of plate/shell thickness and is free of shear locking problems as well as need for shear corrections. When obtaining the time response, solution for an increment of time alternates between the solution of BLM followed by the solution of the energy equation. Details are presented in the paper.

Nucleonic Direct Urca Processes and Cooling of the Massive Neutron Star by Antikaon Condensations

Nucleonic direct Urca processes and cooling of the massive neutron stars are studied by considering antikaon condensations. Calculations are performed in the relativistic mean field and isothermal interior approximations. Neutrino energy losses of the nucleonic direct Urca processes are reduced when the optical potential of antikaons changes from − 80 to − 130 MeV. If the center density of the massive neutron stars is a constant, the masses taper off with the optical potential of antikaons, and neutrino luminosities of the nucleonic direct Urca processes decrease for ρ CN = 0.5 fm − 3 but first increase and then decrease for larger ρ CN . Large optical potential of antikaons results in warming of the nonsuperfluid massive neutron stars. Massive neutron stars turn warmer with the protonic S 0 1 superfluids. However, the decline of the critical temperatures of the protonic S 0 1 superfluids for the large optical potential of antikaons can speed up the cooling of the massive neutron stars.

Privileged Coordinates for Carnot–Carathéodory Spaces of Lower Smoothness

We describe classes of local coordinates on the Carnot–Caratheodory spaces of lower smoothness which permit the homogeneous approximation of quasimetrics and basis vector fields. We establish the minimal smoothness that is required for these classes to coincide with the class of the already-described privileged coordinates in the infinite smoothness case. Moreover, we apply these results to prove the analogs of the available theorems in the case of the canonical coordinates of the second kind. Also, we prove some convergence theorems in quasimetric spaces.

Global dynamical time for binary point-like particle systems

A geometrical construction for a global dynamical time for binary point-like particle systems, modeled by relativistic equations of motions, is presented. Thus, we provide a convenient tool for the calculation of the dynamics of recent models for the dynamics of black holes that use individual proper times. The construction is naturally based on the local Lorentzian geometry of the spacetime considered. Although in this presentation we are dealing with the Minkowskian spacetime, the construction is useful for gravitational models that have as a seed Minkowski spacetime. We present the discussion for a binary system, but the construction is obviously generalizable to multiple particle systems. The calculations are organized in terms of the order of the corresponding relativistic forces. In particular, we improve on the Darwin and Landau–Lifshitz approaches, for the case of electromagnetic systems. We discuss the possibility of a Lagrangian treatment of the retarded effects, depending on the nature of the relativistic forces. The higher-order contractions are based on a Runge–Kutta type procedure, which is used to calculate the quantities at the required retarded time, by increasing evaluations of the forces at intermediate times. We emphasize the difference between approximation orders in field equations and approximation orders in retarded effects in the equations of motion. We show this difference by applying our construction to the binary electromagnetic case.

Lower and upper bound limit analysis via the alternating direction method of multipliers

Abstract Computational limit analysis methods invariably lead to the need to solve a mathematical programming problem. The alternating direction method of multipliers (ADMM) is one versatile and robust technique to solve non-linear convex optimization problems that has recently found applications in a wide range of fields. Its solution scheme, based on an operator splitting algorithm, is not only easy to implement but also suitable to efficiently solve large-scale variational problems. Starting from the ADMM framework, we derive a strict upper bound finite element formulation using a two-(primal)-field approximation, one for the velocity field and the other for the plastic strain rate field. Next, following a similar approach, we develop a novel strict lower bound formulation. Here, the two-(primal)-field model is based on a redundant approximation of the stress field. Duality principles are then explored in order to unify these two formulations.The effectiveness of this approach is demonstrated on test problems and, to conclude, some considerations are made about the performance results.

A classical fluctuation theory of the superfluid, Mott, and normal phases of correlated bosons

We present a method that generalises the standard mean field theory of correlated lattice bosons to include amplitude and phase fluctuations of the U(1) field that induces onsite particle number mixing. We solve the resulting problem, initially, by using a classical approximation for the particle number mixing field and a Monte Carlo treatment of the resulting bosonic model. In two dimensions we obtain Tc scales that dramatically improve on mean field theory and are within about 20% of quantum Monte Carlo estimates at density n = 1. The ground state, however, is still mean field, with an overestimate of the critical interaction, Uc, for the superfluid to Mott transition. Further including gaussian quantum fluctuations strikingly improves the Uc and the overall thermal phase diagram. The approach has a computational cost that is linear in system size, readily generalises to multispecies bosons, disorder, and the presence of traps, and yields real frequency response functions.

A Methodology for Remote Sensing Inter-Turn Fault Events in Power System Air-Core Reactors, via Simulation of Magneto Quasi-Static Fields in 2D FDTD

We present a numerical methodology to estimate the transient fault currents and to simulate the remote sensing of transient fault information embedded in the magnetic field emissions caused by inter-turn shorts in 60 Hz air-core reactors, thru a magneto quasi-static (MQS) field approximation in the method of Finite-Difference Time-Domain (FDTD) in 2-dimensional (2D) space. The MQS 2D FDTD fields of reactor in normal operation are scaled by correlation against an equivalent circuit model that is derived from application of basic physics principles to parameters of the 3D air-core reactor. The proposed multi-scale quasi-static modeling methodology, based on the reduced c modification, provides fine-feature access down to the single-wire level and can efficiently estimate the transient fault fields and currents due to turn-to-turn short in a reactor with core height in several meters, core diameter in meters, wire diameter in millimeters, and number of turns in the thousands, at 60 Hz; this is accomplished by using computational resources of a typical laptop computer within seconds or minutes , as opposed to days that would be otherwise required without the reduced c modification.

Finite elements for problems of the elasticity theory with the discontinuous stress approximation

The paper deals with the development of the finite element models on the basis of stress approximation. At present, the displacementbased finite element method is mainly used for engineering calculations. Finite element formulations in stresses are not so widely spread, but in some cases these formulations can be more effective in particular with respect to the calculating stresses and also obtaining a two-sided estimate of the exact solution of the problem. The finite element models based on the approximation of discontinuous stress fields and the use of the penalty function method to satisfy the equilibrium equations are considered. It is shown that the continuity of both normal and tangential stresses only on the adjacent sides of the finite elements contributes to the expansion of the class of statically admissible stress fields. At the same time, the consistent approximation is provided, both of the main part of the functional of additional energy, and its penalty part. The necessary matrix relations for rectangular and triangular finite elements are obtained. The effectiveness of the developed models is illustrated by numerical studies. The calculation results were compared with the solution on the FEM in displacements, as well as with the results obtained using other schemes of approximating the stresses in the finite element. It is shown that the model of discontinuous stress approximations gives the bottom convergence of the solution, both in stresses and in displacements. At the same time, the accuracy on the stresses here is much higher than in the displacement-based FEM or when using conventional stress approximation schemes.

Convergence of Markovian stochastic approximation for Markov random fields with hidden variables

This paper studies the convergence of the stochastic algorithm of the modified Robbins–Monro form for a Markov random field (MRF), in which some of the nodes are clamped to be observed variables while the others are hidden ones. Based on the theory of stochastic approximation, we propose proper assumptions to guarantee the Hölder regularity of both the update function and the solution of the Poisson equation. Under these assumptions, it is proved that the control parameter sequence is almost surely bounded and accordingly the algorithm converges to the stable point of the log-likelihood function with probability [Formula: see text].

Enhancement of directivity of dipole antenna by a complex conjugate cylinder

ABSTRACT The directional properties of a dipole antenna are studied by placing it in the vicinity of a complex conjugate cylinder. An exact formal solution for the fields is obtained via the differential equation approach. The far field approximation is obtained by asymptotic analysis. The variation of radiation patterns with the imaginary part of permittivity and/or permeability is observed and the results are compared with the lossless dielectric. It is observed that the directivity of the antenna is enhanced in the presence of the cylinder.

Parameter dependence of acoustic mode quantities in an idealized model for shallow-water nonlinear internal wave ducts.

Nonlinear internal waves in shallow water have significant acoustic impacts and cause three-dimensional ducting effects, for example, energy trapping in a duct between curved wavefronts that propagates over long distances. A normal mode approach applied to a three-dimensional idealized parametric model [Lin, McMahon, Lynch, and Siegmann, J. Acoust. Soc. Am. 133(1), 37-49 (2013)] determines the dependence of such effects on parameters of the features. Specifically, an extension of mode number conservation leads to convenient analytical formulas for along-duct (angular) acoustic wavenumbers. The radial modes are classified into five types depending on geometric characteristics, resulting in five distinct formulas to obtain wavenumber approximations. Examples of their dependence on wavefront curvature and duct width, along with benchmark comparisons, demonstrate approximation accuracy over a broad range of physical values, even including situations where transitions in mode types occur with parameter changes. Horizontal-mode transmission loss contours found from approximate and numerically exact wavenumbers agree well in structure and location of intensity features. Cross-sectional plots show only small differences between pattern phases and amplitudes of the two calculations. The efficiency and accuracy of acoustic wavenumber and field approximations, in combination with the mode-type classifications, suggest their application to determining parameter sensitivity and also to other feature models.

Converging photospheric vortex flows close to the polarity inversion line of a fully emerged active region

Abstract. We report on the occurrence of vortexes in flow fields obtained from the evolution of the line-of-sight component of the photospheric magnetic field in a region around the polarity inversion line (PIL) of a fully emerged active region. Based on a local linear approximation for the flow field, we identify the presence of critical points and classify them according to the eigenvalues of the Jacobian matrix of the linear transformation. Converging vortexes are associated with the presence of a particular kind of critical point, known as the attracting focus. We identified 12 converging vortexes in the analyzed period and detected the occurrence of other types of critical points, which indicate the complexity of the flow field around the PIL. The detected vortexes show a clockwise preferred sense of rotation with approximately 67 % of the cases. A geometrical analysis of the velocity structures produced an average value of D‾=1.63±0.05 for the fractal dimension, which is very close to the one obtained for isotropic homogeneous turbulence (D=5/3). This suggests that the flow around the PIL is turbulent in nature.

An improved MoM-PO hybrid method for scattering from multiple 3-D objects above the 2-D random conducting rough surface

ABSTRACTAn improved hybrid scheme combining the method of moment (MoM) and the physical optic (PO) is first presented to investigate scattering from multiple 3-D conducting objects above the electrically large conducting rough surface. First, the composite model is constructed by dividing rough surface into PO area and multiple objects into MoM area, and each object is divided into different area further. Next, the electric current in PO area is obtained through the PO approximation and the electric current in MoM area is computed by MoM. The contribution of PO area is coupled into impedance matrix of MoM. Domain distribution method is introduced, by which electric field integral equations are established on the surface of each object in MoM area and solved at the same time. Vector–matrix multiplication between the objects and the rough surface is accelerated by fast far field approximation, working by reducing the interaction between source point and observation point. What’s more, adaptive integral method is used to accelerate the MoM part, by which the computing complexity is reduced from O(M2) to O(MlogM). Compared with traditional coupling MoM-PO, this improved hybrid method proves to be much faster and has the same accuracy. Numerical examples are presented to analyze the composite scattering from multiple objects above rough surface under different conditions.

Temperature Distribution in the “Material-Coating” Interface from a Fast-Moving Heat Emission Source for Electromagnetic Surfacing

During simulation of the surfacing process, it is proposed to present the heat emission source in the form of the system of instantaneous point sources flickering for some time; and the period between flashes tends to zero. The final results of the temperature distribution are determined by summing the solitary impacts according to the proposed computational pattern. The obtained characteristics and analytical curves allow presenting, at a first approximation, the value and intensity of the temperature fields in the working zone during the electromagnetic surfacing of the large size blanks with sufficient heat removal from the restored surface. The proposed method may be applied for repair and modernization of the railway vehicles elements.

Dipole Approximation for Electrically Small Loop Antennas

An elementary magnetic emitter is considered as an approximation for the variable magnetic field of an electrically small radiating loop antenna. The frequency limits for applicability of the stationary dipole model are studied. Approximate formulas are obtained for characterizing the difference between the magnetic field of a circular loop antenna and the magnetic field of the equivalent point source.

Beyond-mean-field effective masses in the nuclear Fermi liquid from axial breathing modes

Axial breathing modes are studied within the nuclear energy--density--functional theory to discuss the modification of the nucleon effective mass produced beyond the mean--field approximation. This analysis is peformed with the subtracted second random--phase--approximation (SSRPA) model applied to two nuclei, $^{48}$Ca and $^{90}$Zr. Analyzing the centroid energies of axial breathing modes obtained with the mean--field--based random--phase approximation and with the beyond--mean--field SSRPA model, we estimate the modification (enhancement) of the effective mass which is induced beyond the mean field. This is done by employing a relation, obtained with the Landau's Fermi liquid theory, between the excitation frequency of axial modes to $\sqrt{m/m^*}$, where $m$ ($m^*$) is the bare (effective) mass. Such an enhancement of the effective mass is discussed in connection with the renormalization of single--particle excitation energies generated by the energy--dependent SSRPA self-energy correction. We find that the effective beyond--mean--field compression of the single--particle spectrum produced by the self--energy correction is coherent with the increase of the effective mass estimated from the analysis of axial breathing modes.