Arbitrary Spatial Points Research Articles

Multi‐Spacecraft Magnetic Field Reconstructions: A Cross‐Scale Comparison of Methods

AbstractSpace plasma studies frequently use in situ magnetic field measurements taken from many spacecraft simultaneously. A useful data product of these measurements is the reconstructed magnetic field in a volume near the spacecraft observatory. We compare a standard Linear method of computing the magnetic field at arbitrary spatial points to two novel approaches: a Radial Basis Function interpolation and a time‐dependent 2D inverse distance weighted interpolation scheme called Timesync. These three methods, which only require in situ measurements of the magnetic fields and bulk plasma velocities at a sparse set of spatial points, are implemented on synthetic data drawn from a time‐evolving numerical simulation of plasma turbulence. We compare both the topology of the reconstructed field to the ground truth of the simulation and the statistics of the fluctuations found in the reconstructed field to those from the simulated turbulence. We conclude that the Radial Basis Function and Timesync methods outperform the Linear method in both topological and statistical comparisons.

Terahertz Spatiotemporal Wave Synthesis in Random Systems.

Complex media have emerged as a powerful and robust framework to control light-matter interactions designed for task-specific optical functionalities. Studies on wavefront shaping through disordered systems have demonstrated optical wave manipulation capabilities beyond conventional optics, including aberration-free and subwavelength focusing. However, achieving arbitrary and simultaneous control over the spatial and temporal features of light remains challenging. In particular, no practical solution exists for field-level arbitrary spatiotemporal control of wave packets. A new paradigm shift has emerged in the terahertz frequency domain, offering methods for absolute time-domain measurements of the scattered electric field, enabling direct field-based wave synthesis. In this work, we report the experimental demonstration of field-level control of single-cycle terahertz pulses on arbitrary spatial points through complex disordered media.

Peculiarities in the Transformation of the Profile of Acoustic Nonlinear Waves Reflected from a Stepped Structure

The article presents the results of studying the reflection of an intense acoustic beam from stepped structures. The case of high Reynolds numbers is considered, when a sawtooth wave profile formed in the incident beam, and an obstacle in the form of a step was located normal to the acoustic axis and behind the discontinuity coordinate. When reflected from the obstacle, the acoustic beam incident on it splits into two parts, between which there is a path difference, specified by the stepped structure itself. The experiment focused on obstacles that create a path difference between the two parts of the beam during reflection, equal to 0, λ/3, λ/2, λ, etc. A broadband membrane hydrophone was used to record the shape of the profile of nonlinear waves of the incident and reflected acoustic beams at an arbitrary spatial point. This made it possible to analyze the evolution of the beam shape with increasing distance from the obstacle, as well as to study its transverse structure. The effect of doubling the characteristic frequency of a signal as an acoustic beam is reflected from a stepped structure is shown, which creates a path difference of λ/2 between the two parts of the reflected beam. It is demonstrated that the dynamics of nonlinear effects in intense beams reflected from stepped structures is similar to the transformation of the profile of acoustic waves generated by dual-frequency pump signals.

Onset of synchronization in coupled Mixmaster oscillators.

We consider the problem of asymptotic synchronization of different spatial points coupled to each other in inhomogeneous space-time and undergoing chaotic Mixmaster oscillations towards the singularity. We demonstrate that for couplings larger than some threshold value, two Mixmaster spatial points [Formula: see text], with [Formula: see text] in the past of [Formula: see text], synchronize and thereby proceed in perfect unison towards the initial singularity. We further show that there is a Lyapunov function for the synchronization dynamics that makes different spatial points able to synchronize exponentially fast in the past direction. We provide an elementary proof of how an arbitrary spatial point responds to the mean field created by the oscillators, leading to their direct interaction through spontaneous synchronization. These results ascribe a clear physical meaning of early-time synchronization leading to a resetting effect for the two BKL maps corresponding to two distinct oscillating spatial points, as the two maps converge to each other to become indistinguishable at the end of synchronization. Our results imply that the universe generically organizes itself through simpler, synchronized, states as it approaches the initial singularity. A discussion of further implications of early-time inhomogeneous Mixmaster synchronization is also provided. This article is part of the theme issue 'The future of mathematical cosmology, Volume 1'.

The fraction of overlapping interphase around 2D and 3D polydisperse non-spherical particles: Theoretical and numerical models

The fraction of interphase is an important microstructure parameter in the prediction of macroscopic properties of particulate composites. Currently, some researchers have presented theoretical and numerical investigations on the interphase fraction for spherical particle systems, and even quantify the influence of interphase fraction on the overall elastic and transport properties of particulate composites. However, the overlapping interphase fraction in polydisperse non-spherical particle systems is still an open issue. In this work, a generic theoretical model is formulated to derive the overlapping interphase fraction for polydisperse 2D non-circular and 3D non-spherical particle systems by means of the statistical geometry of composites. In this model, the morphology of interphase coated onto the surface of non-spherical particles can be characterized by circularity and sphericity of particles that are important parameters to describe the shape of particles. On the other hand, numerical simulations for the one-point probability function of interphase are presented to verify the proposed theoretical framework. In the numerical simulations, a novel algorithm is developed by reducing the problem of identifying the precise location between an arbitrary spatial point and interphase to the basic issue of finding the distance from the point to the surface of particles. If the distance is less than the interphase thickness, the point definitely locates inside interphase. In addition, the algorithm can be further used to detect the overlap between adjacent ellipsoidal particles (2D ellipses). Moreover, a variety of particle shapes (such as regular polygons and ellipses with the same circularity, and regular polyhedrons and ellipsoids with the same sphericity) are taken into account to generate particle packing structures. Then, the fraction of overlapping interphase in each packing structure is statistically obtained. Results show that statistical values are consistent with their theoretical values under the same conditions. This validates the reliability of the theoretical framework. Finally, the effects of particle size distributions and interphase thicknesses on the interphase fraction are investigated. It can be found that the interphase fraction increases with the increase of particle volume fraction, particle fineness and interphase thickness.

Influence of spin relaxation on magnetoresistance

We represent the spin-dependent transport across a pseudospin-valve structure as described by the spin drift-diffusion (SDD) theory by an effective two-current model, in which the spin relaxation effects are globally absorbed into the two effective branch resistances. Our approach has eliminated the need for “spin flip” resistances interconnecting the two spin branches, which have the disadvantage of artificially localizing the effects of spin relaxation to arbitrary spatial points. We confirm the accuracy of our effective two-current model with the full numerical SDD solution. Based on our model, we found that (i) the overall magnetoresistance (MR) is much more sensitive to the spin relaxation effect in the nonmagnetic (NM) layer, compared to that in the ferromagnetic (FM) layers, and that (ii) the effective spin relaxation length λE in the NM layer is intrinsically linked to the conductivity σN,F of the NM and FM layers. We found that λE=λN∕(η)1∕2, where λN is the nominal spin relaxation length in the NM layer and η=(σN∕σF). The analytical link between spin relaxation and conductivity explains the previously described anomalous suppression of MR, when the conductivity ratio η exceeds a certain critical value ηC.

The well—posedness of the formulation of diffraction problems reduced to Fredholm integral equations of the first kind with a smooth kernel

The well-posedness of diffraction problems that are reduced to Fredholm integral equations of the first kind with a smooth kernel is analyzed. The auxiliary source method and the method of extended boundary conditions, both of which involve solution of Fredholm integral equations of the first kind with a smooth kernel, are applied to show for specific examples that algorithms of calculation of all physically significant quantities—the scattering pattern, the field at an arbitrary spatial point except current-carrier points, etc.—are quite stable and allow for computation of the aforementioned quantities with a preassigned accuracy.

Statistical Mechanics: Undamaged ⇐-radiation-⇒ Damaged Atomic Lattice Density Evolution and Stochastic Deformation Functional

AbstractThe deformation kinematics for radiation damage response of bulk materials is presently semi-empirical and phenomenological based on a continuum mechanics supposition: there exists a function space of continuous functions to describe material displacement, strain, strain-rate metrics by using the mathematics of differential calculus. Existing data being assembled from tests on nano-length-scale(NLS) samples provide objective evidence that the continuum mechanics supposition is not an adequate generic mathematical description for radiation damage response in surface-dominated material structures at NLS. An alternative approach will be described that uses concepts and methods from classical statistical mechanics and describe deformation kinematics as a stochastic accumulation of discrete damage events at atomic lattice nano-length-scales. Although radiation damage deformation at a lattice length-scale in solids is mechanistically different from velocity scattering developed by Boltzmann for a kinetic theory of gases, the two problem areas are technically similar and in some simply cases there are useful mathematical analogs. The technical similarities and mathematical analogs will be used to define probability density functions (number per unit volume functions) for undamaged and damaged “size and size change” lattice species (similarity to a probability density function for atomic velocities in gas theory). In general, equations for undamaged and damaged lattice density function evolution are Boltzmann-type equations, which can be approximated and solved for simple cases of radiation induced material damage. Using a path integral approach and the two probability density functions, a stochastic functional will be derived for the relative deformation between any two arbitrary spatial points in a radiation damaged material. Given the relative deformation as an explicit functional of the undamaged and damaged lattice density functions, the kinematics metrics of relative velocity, strain, strain rate, etc., will also be functionals. In the case of radiation damage and annealing, the two lattice density functions are analog expressions to those commonly used to model “birth and death” population evolution.

Buffeting response of long-span cable-supported bridges under skew winds. Part 1: theory

A finite-element-based framework for buffeting analysis of long-span cable-supported bridges under skew winds is developed in the frequency domain utilizing the linear quasi-steady theory and the strip theory of aerodynamics in conjunction with the pseudo excitation method. A set of universal expressions for six components of buffeting forces is first derived in association with oblique cross-sections of bridge components, in which the buffeting forces are formed with respect to the wind coordinate system and then converted to those with respect to the structural coordinate system. Skew mean wind and three orthogonal components of velocity fluctuations can thus be easily handled without any further decomposition. The coherence between velocity fluctuations of wind turbulence at any two arbitrary spatial points is considered in the global wind coordinate system rather than in the global structural coordinate system. Aeroelastic stiffness and damping matrices due to self-excited forces are then taken into consideration in terms of the 18 flutter derivatives with respect to the oblique cross-sections. The pseudo-excitation method is finally employed to solve efficiently the fully coupled 3D buffeting problem of long-span cable-supported bridges under skew winds with the effects of multi-modes and spatial modes, inter-mode coupling and aerodynamic coupling, and the interaction among major bridge components being naturally included.

The balanced allocation of customers to multiple distribution centers in the supply chain network: a genetic algorithm approach

In a typical location–allocation problem, customer demand data are often aggregated according to some arbitrary spatial points (e.g. population centers) or boundaries (e.g. census districts). Since such points or boundaries do not represent true sources of customer demands, allocation of aggregated customers to distribution centers can lead to underutilization of distribution centers and deterioration of customer services. In an effort to design a supply chain network that maintains the best balance of transportation cost and customer service, this paper proposes a new model based on naı̈ve balanced star spanning forest formulation. This model goes beyond traditional mathematical programming by incorporating a genetic algorithm that is proven to be effective in dealing with the NP-hard problem.

An adaptive approach with the Element-Free-Galerkin method

The Element-Free-Galerkin-method may be regarded as an alternative to the Finite-Element-method especially for problems with discontinuities, e.g. crack propagation problems. The EFG-method differs from the FEM by using the Moving-Least-Squares-interpolation. The behaviour of this interpolation is strongly influenced by a weighting function, which rules the influence of nodal variables on variables in arbitrary spatial points. With an appropriate selection of the weighting function derivatives of field functions of any desired order are continuous throughout the problem domain within the MLS-interpolation. Hence, gradients of stresses and strains may be calculated throughout the problem domain with a high accuracy. Furthermore, the configuration of nodes is quite flexible, as nodes are not ordered by an element connectivity. Nodes are easily introduced, moved or discarded. The latter characteristics make the EFG-method especially suitable for adaptive schemes. A scheme based on strain gradients is discussed in this paper. It is applied to several linear and physically nonlinear problems with high stress-resp. strain gradients and singularities. Continued mesh refinement in areas of high gradients is derived. The convergence behaviour is investigated for cases, where analytical solutions are available.

Directional Wave Characteristics of Multi-Directional Wave Generator based on Numerical Simulation

Many experiments had been carried out in the long experimental towing tank in Yokohama National University (YNU) with generating directional spectrum waves by segmented and independent wave makers and using side-wall reflections positively. It is important to make more accurate generation of the directional spectrum waves considering the increasing demands for experiments among such waves.To accomplish these subjects, present paper investigates the characteristics of directional distribution by carrying out numerical generation of directional spectrum waves and its analysis for the case of without and with side-wall reflection. This calculation is based on the superposition of ring waves generated by the periodic line source distributions representing each wave maker unit. Mirror images are also introduced for considering reflections of side-wall including the ratio of reflection (reflection coefficient) because directional waves will not be reflected perfectly from real side-wall. In addition to this, directivity (Dd) and tapering effect for the distribution of source strength will be evaluated to generate more accurate directional spectrum waves. Especially, influence of spurious waves generated by the combined effect of finite width of segmented wave maker, wave length and main wave propagating direction will be investigated.To analyze directional spectrum waves, we use MLM (Maximum Likelihood Method) from calculated time series of wave elevation and two component wave slopes at the arbitrary spatial point. This corresponds to the Laser Beam Type Surface Wave Probe developed in Y. N. U, and reliability of this method was examined already.

Defects in Aluminum: A Density Functional Study

ABSTRACTWe describe a new method of examining defects and their interactions with each other at a microscopic level of detail. This involves efficiently calculating local properties at arbitrary spatial points, applicable in periodic supercell calculations. In particular, we have identified two quantities, the local energy density, ε(r) and the local stress density, σαβ(r), which are constrained to yield the total energy and the average macroscopic stress tensor, respectively, when integrated over the entire volume of the supercell. In systems with defects, these microscopic quantities provide important insights about the local nature and environment of defects. For the test case of bulk Al with a point defect, we demonstrate that these concepts result in meaningful local quantities characteristic to the point defect. We propose to use these methods to study the microscopic nature of vacancies at a grain boundary and their interaction with each other.

Four-Center Molecular Integrals in Quantum Chemistry

A new method is presented for the calculation of two-electron interaction integrals for Slater-type orbitals. The method is suitable for any form of interelectronic interaction and applies to orbitals with arbitrary integral quantum numbers, located at arbitrary spatial points with arbitrary relative orientations. Computational work is reduced to a minimum for inverse-power interactions, since the analysis utilizes existing programs for two-center overlap integrals.

Multicenter Integrals in Quantum Mechanics. II. Evaluation of Electron-Repulsion Integrals for Slater-Type Orbitals

A unified method for the evaluation of electron-repulsion integrals for Slater-type orbitals is described. This method applies to every electron-repulsion integral needed for polyatomic molecule calculations, and is sufficiently general to handle integrals over orbitals with higher quantum numbers, located at arbitrary spatial points with arbitrary relative orientations. Computation programs have been prepared to implement this analysis with emphasis on both the requirements of speed and accuracy in evaluating the large number of electron-repulsion integrals required for a polyatomic calculation. Comparisons with other methods are given which indicate that this unified approach can result in at least an order-of-magnitude saving in computation time for large molecular systems.