Finite Spatial Extent Research Articles

Reduced energies for thin ferromagnetic films with perpendicular anisotropy

We derive four reduced two-dimensional models that describe, at different spatial scales, the micromagnetics of ultrathin ferromagnetic materials of finite spatial extent featuring perpendicular magnetic anisotropy and interfacial Dzyaloshinskii–Moriya interaction. Starting with a microscopic model that regularizes the stray field near the material’s lateral edges, we carry out an asymptotic analysis of the energy by means of [Formula: see text]-convergence. Depending on the scaling assumptions on the size of the material domain versus the strength of dipolar interaction, we obtain a hierarchy of the limit energies that exhibit progressively stronger stray field effects of the material edges. These limit energies feature, respectively, a renormalization of the out-of-plane anisotropy, an additional local boundary penalty term forcing out-of-plane alignment of the magnetization at the edge, a pinned magnetization at the edge, and, finally, a pinned magnetization and an additional field-like term that blows up at the edge, as the sample’s lateral size is increased. The pinning of the magnetization at the edge restores the topological protection and enables the existence of magnetic skyrmions in bounded samples.

Bell Instability–mediated Diffusive Shock Acceleration at Supernova Blast Wave Shock Propagating in the Interstellar Medium

Supernova blast wave shock is a very important site of cosmic-ray acceleration. However, the detailed physical process of acceleration, in particular, nonlinear interplay between cosmic-ray streaming and magnetic field amplification, has not been studied under a realistic environment. In this paper, using a unique and novel numerical method, we study cosmic-ray acceleration at supernova blast wave shock propagating in the interstellar medium with well-resolved magnetic field amplification by nonresonant hybrid instability (or Bell instability). We find that the magnetic field is mildly amplified under typical interstellar medium conditions that leads to maximum cosmic-ray energy ≃30 TeV for supernova remnants with age ≃1000 yr consistent with gamma-ray observations. The strength of the amplified magnetic field does not reach the so-called saturation level because the cosmic-ray electric current toward the shock upstream has a finite spatial extent, by which Bell instability cannot experience many e-folding times.

Simulating room transfer functions between transducers mounted on audio devices using a modified image source method.

The image source method (ISM) is often used to simulate room acoustics due to its ease of use and computational efficiency. The standard ISM is limited to simulations of room impulse responses between point sources and omnidirectional receivers. In this work, the ISM is extended using spherical harmonic directivity coefficients to include acoustic diffraction effects. These effects occur in practice when transducers are mounted on audio devices of finite spatial extent, e.g., modern smart speakers with loudspeakers and microphones. The proposed method is verified using finite element simulations of various loudspeaker and microphone configurations in a shoebox-shaped room. It is shown that the accuracy of the proposed method is related to the sizes, shapes, number, and positions of the devices inside a room. A simplified version of the proposed method, which can significantly reduce computational effort, is also presented. The proposed method and its simplified version can simulate room transfer functions more accurately than currently available image source methods and can aid the development and evaluation of speech and acoustic signal processing algorithms, including speech enhancement, acoustic scene analysis, and acoustic parameter estimation.

Kinetic simulations of solar wind plasma irregularities crossing the Hermean magnetopause

Context. The physical mechanisms that favor the access of solar wind plasma into the magnetosphere have not been entirely elucidated to date. Studying the transport of finite-sized magnetosheath plasma irregularities across the magnetopause is fundamentally important for characterizing the Hermean environment (of Mercury) as well as for other planetary magnetic and plasma environments. Aims. We investigate the kinetic effects and their role on the penetration and transport of localized solar wind or magnetosheath plasma irregularities within the Hermean magnetosphere under the northward orientation of the interplanetary magnetic field. Methods. We used three-dimensional (3D) particle-in-cell (PIC) simulations adapted to the interaction between plasma elements (irregularities or jets) of a finite spatial extent and the typical magnetic field of Mercury’s magnetosphere. Results. Our simulations reveal the transport of solar wind plasma across the Hermean magnetopause and entry inside the magnetosphere. The 3D plasma elements are braked and deflected in the equatorial plane. The entry process is controlled by the magnetic field gradient at the magnetopause. For reduced jumps of the magnetic field (i.e., for larger values of the interplanetary magnetic field), the magnetospheric penetration is enhanced. The equatorial dynamics of the plasma element is characterized by a dawn-dusk asymmetry generated by first-order guiding center drift effects. More plasma penetrates into the dusk flank and advances deeper inside the magnetosphere than in the dawn flank. Conclusions. The simulated solar wind or magnetosheath plasma jets can cross the Hermean magnetopause and enter into the magnetosphere, as described by the impulsive penetration mechanism.

The coset construction for particles of arbitrary spin

When a Poincaré-invariant system spontaneously breaks continuous internal symmetries, Goldstones’ theorem demands the existence of massless, spin-zero excitations in a one-to-one correspondence with the broken symmetry generators. When a system spontaneously breaks Poincaré symmetry, however, the kinds of excitations that satisfy Goldstone’s theorem can be quite unusual. In particular, they may have any spin and need not be particles or even quasiparticles. The standard coset construction used to formulate effective actions of Goldstones, however, is rather restrictive and is incapable of generating the full spectrum of possibilities allowed by Goldstone’s theorem. We propose a (partial) remedy to this problem by postulating a novel coset construction for systems that spontaneously break Poincaré symmetry. This new construction is capable of generating effective actions with a wide range of Goldstone excitations — including fermionic degrees of freedom — even when all symmetries are bosonic. To demonstrate its utility, we focus on constructing effective actions for point particles of various spins. We recover the known result that a particle of spin s requires an mathcal{N} = 2s supersymmetric worldline reparameterization gauge symmetry, which we implement at the level of the coset construction. In the process, we discover that massless particles require a novel kind of inverse Higgs constraint that bears some resemblance to the dynamical inverse Higgs constraints that appear in certain fermi liquid effective field theories. We then consider particles that, in addition to quantum spin, have finite spatial extent and are free to rotate. We derive a novel action for such particles and find a ‘spin-orbital’ coupling between the intrinsic quantum spin and the physical-rotation degrees of freedom.

Discrete Approximations of Acoustic Source Distributions

The modeling of source a distributions of finite spatial extent in ultrasound and medical imaging applications is a problem of longstanding interest. In time-domain methods, such as the finite-difference time-domain or pseudospectral approaches, one requirement is the representation of such distributions over a grid, normally Cartesian. Various artifacts, including staircasing errors, can arise. In this short contribution, the problem of the representation of distribution over a grid is framed as an optimization problem in the Fourier domain over a preselected set of grid points, thus maintaining control over computational cost and allowing the fine-tuning of the optimization to the wavenumber range of interest for a particular numerical method. Numerical results are presented in the important special case of the spherical cap or bowl source.

Modeling continuous source distributions in wave-based virtual acoustics.

All acoustic sources are of finite spatial extent. In volumetric wave-based simulation approaches (including, e.g., the finite difference time domain method among many others), a direct approach is to represent such continuous source distributions in terms of a collection of point-like sources at grid locations. Such a representation requires interpolation over the grid and leads to common staircasing effects, particularly under rotation or translation of the distribution. In this article, a different representation is shown, based on a spherical harmonic representation of a given distribution. The source itself is decoupled from any particular arrangement of grid points, and is compactly represented as a series of filter responses used to drive a canonical set of source terms, each activating a given spherical harmonic directivity pattern. Such filter responses are derived for a variety of commonly encountered distributions. Simulation results are presented, illustrating various features of such a representation, including convergence, behaviour under rotation, the extension to the time varying case, and differences in computational cost relative to standard grid-based source representations.

Looking for MACHOs in the spectra of fast radio bursts

ABSTRACT We explore a novel search strategy for dark matter in the form of massive compact halo objects (MACHOs) such as primordial black holes or dense mini-haloes in the mass range from $10^{-4}\, \mathrm{M}_{\odot }$ to $0.1\, \mathrm{M}_{\odot }$. These objects can gravitationally lens the signal of fast radio bursts (FRBs), producing a characteristic interference pattern in the frequency spectrum, similar to the previously studied femtolensing signal in gamma-ray burst spectra. Unlike traditional searches using microlensing, FRB lensing will probe the abundance of MACHOs at cosmological distance scales (∼Gpc) rather than just their distribution in the neighbourhood of the Milky Way. The method is thus particularly relevant for dark mini-haloes, which may be inaccessible to microlensing due to their finite spatial extent or tidal disruption in galaxies. We find that the main complication in FRB lensing will be interstellar scintillation in the FRB’s host galaxy and in the Milky Way. Scintillation is difficult to quantify because it heavily depends on turbulence in the interstellar medium, which is poorly understood. We show that, nevertheless, for realistic scintillation parameters, FRB lensing can set competitive limits on compact dark matter object, and we back our findings with explicit simulations.

Phase transitions in finite size systems

We follow recent developments of a finite size thermal field theoretic formalism, which is mainly relevant to the investigation of small size corrections to the thermodynamical properties of the quark-gluon plasma. In doing so, we rely on statistical mechanics and large deviation theory arguments, and investigate geometrically confined systems of infinite volume V with a finite spatial extent L. More specifically, we focus on systems in contact with a heat bath as well as on isolated ones. We find and present in detail the characteristic behaviors of a first and a second order phase transition, respectively. In the former case, we establish a connection between the phase transition and the mechanical support of the system. In the latter one, we identify a critical length Lc~(V/EL)1/3, where E is the total energy of the system which is fixed. We also briefly comment on the relevance of our findings, for respectively both the Casimir experiments and the future quark-gluon plasma phenomenology.

Evolution of charge fluctuations and correlations in the hydrodynamic stage of heavy ion collisions

Charge fluctuations for a baryon-neutral quark-gluon plasma have been calculated in lattice gauge theory. These fluctuations provide a well-posed rigorous representation of the quark chemistry of the vacuum for temperatures above T_c >~ 155 MeV. Due to the finite lifetime and spatial extent of the fireball created in relativistic heavy ion collisions, charge-charge correlations can only equilibrate for small volumes due to the finite time required to transport charge. This constraint leads to charge correlations at finite relative position that evolve with time. The source and evolution of such correlations is determined by the evolution of the charge fluctuation and the diffusion constant for light quarks. Here, calculations are presented for the evolution of such correlations superimposed onto hydrodynamic simulations. Results are similar to preliminary measurements from STAR, but significant discrepancies remain.

Nonperturbative evaluation for anomalous dimension in 2-dimensional O(3) sigma model

We calculate the wave-function renormalization in 2-dimensional O(3) sigma model, non- perturbatively. It is evaluated in a box with a finite spatial extent. We determine the anomalous dimension in the finite volume scheme through an analysis of the step scaling function. Results are compared with a perturbative evaluation, and the reasonable behavior is confirmed.

Faraday-Shielded dc Stark-Shift-Free Optical Lattice Clock.

We demonstrate the absence of a dc Stark shift in an ytterbium optical lattice clock. Stray electric fields are suppressed through the introduction of an in-vacuum Faraday shield. Still, the effectiveness of the shielding must be experimentally assessed. Such diagnostics are accomplished by applying high voltage to six electrodes, which are grounded in normal operation to form part of the Faraday shield. Our measurements place a constraint on the dc Stark shift at the 10^{-20} level, in units of the clock frequency. Moreover, we discuss a potential source of error in strategies to precisely measure or cancel nonzero dc Stark shifts, attributed to field gradients coupled with the finite spatial extent of the lattice-trapped atoms. With this consideration, we find that Faraday shielding, complemented with experimental validation, provides both a practically appealing and effective solution to the problem of dc Stark shifts in optical lattice clocks.

Phase-and-amplitude recovery from a single phase-contrast image using partially spatially coherent x-ray radiation

A simple method of phase-and-amplitude extraction is derived that corrects for image blurring induced by partially spatially coherent incident illumination using only a single intensity image as input. The method is based on Fresnel diffraction theory for the case of high Fresnel number, merged with the space-frequency description formalism used to quantify partially coherent fields and assumes the object under study is composed of a single-material. A priori knowledge of the object’s complex refractive index and information obtained by characterizing the spatial coherence of the source is required. The algorithm was applied to propagation-based phase-contrast data measured with a laboratory-based micro-focus x-ray source. The blurring due to the finite spatial extent of the source is embedded within the algorithm as a simple correction term to the so-called Paganin algorithm and is also numerically stable in the presence of noise.

From discrete to continuous description of spherical surface charge distributions.

The importance of electrostatic interactions in soft matter and biological systems can often be traced to non-uniform charge effects, which are commonly described using a multipole expansion of the corresponding charge distribution. The standard approach when extracting the charge distribution of a given system is to treat the constituent charges as points. This can, however, lead to an overestimation of multipole moments of high order, such as dipole, quadrupole, and higher moments. Focusing on distributions of charges located on a spherical surface - characteristic of numerous biological macromolecules, such as globular proteins and viral capsids, as well as of inverse patchy colloids - we develop a novel way of representing spherical surface charge distributions based on the von Mises-Fisher distribution. This approach takes into account the finite spatial extension of individual charges, and leads to a simple yet powerful way of describing surface charge distributions and their multipole expansions. In this manner, we analyze charge distributions and the derived multipole moments of a number of different spherical configurations of identical charges with various degrees of symmetry. We show how the number of charges, their size, and the geometry of their configuration influence the behavior and relative importance of multipole magnitudes of different order. Importantly, we clearly demonstrate how neglecting the effect of charge size leads to an overestimation of high-order multipoles. The results of our work can be applied to construct analytical models of electrostatic interactions and multipole expansion of charged particles in diverse soft matter and biological systems.

Spin Fluctuations in the 0.7 Anomaly in Quantum Point Contacts.

It has been argued that the 0.7 anomaly in quantum point contacts (QPCs) is due to an enhanced density of states at the top of the QPC barrier (the van Hove ridge), which strongly enhances the effects of interactions. Here, we analyze their effect on dynamical quantities. We find that they pin the van Hove ridge to the chemical potential when the QPC is subopen, cause a temperature dependence for the linear conductance that qualitatively agrees with experiments, strongly enhance the magnitude of the dynamical spin susceptibility, and significantly lengthen the QPC traversal time. We conclude that electrons traverse the QPC via a slowly fluctuating spin structure of finite spatial extent.

On indirect noise in multicomponent nozzle flows

A one-dimensional, unsteady nozzle flow is modelled to identify the sources of indirect noise in multicomponent gases. First, from non-equilibrium thermodynamics relations, it is shown that a compositional inhomogeneity advected in an accelerating flow is a source of sound induced by inhomogeneities in the mixture (i) chemical potentials and (ii) specific heat capacities. Second, it is shown that the acoustic, entropy and compositional linear perturbations evolve independently from each other and they become coupled through mean-flow gradients and/or at the boundaries. Third, the equations are cast in invariant formulation and a mathematical solution is found by asymptotic expansion of path-ordered integrals with an infinite radius of convergence. Finally, the transfer functions are calculated for a supersonic nozzle with finite spatial extent perturbed by a methane–air compositional inhomogeneity. The proposed framework will help identify and quantify the sources of sound in nozzles with relevance, for example, to aeronautical gas turbines.

On indirect noise in multicomponent nozzle flows

A one-dimensional, unsteady nozzle flow is modelled to identify the sources of indirect noise in multi-component gases. First, from non-equilibrium thermodynamics relations, it is shown that a compositional inhomogeneity advected in an accelerating flow is a source of sound induced by inhomogeneities in the mixture (i) chemical potentials and (ii) specific heat capacities. Second, it is shown that the acoustic, entropy and compositional linear perturbations evolve independently from each other and they become coupled through mean-flow gradients and/or at the boundaries. Third, the equations are cast in invariant formulation and a mathematical solution is found by asymptotic expansion of path-ordered integrals with an infinite radius of convergence. Finally, the transfer functions are calculated for a supersonic nozzle with finite spatial extent perturbed by a methane-air compositional inhomogeneity. The proposed framework will help identify and quantify the sources of sound in nozzles with relevance, for example, to aeronautical gas turbines.

High-contrast self-imaging with ordered optical elements

Creating arbitrary light patterns finds applications in various domains including lithography, beam shaping, metrology, sensing and imaging. We study the formation of high-contrast light patterns that are obtained by transmission through an ordered optical element based on self-imaging.By applying the phase-space method, we explain phenomena such as the Talbot and the angular Talbot effects. We show that the image contrast is maximum when the source is either a plane wave or a point source, and it has a minimum for a source with finite spatial extent. We compare these regimes and address some of their fundamental differences. Specifically, we prove that increasing the source divergence reduces the contrast for the plane wave illumination but increases it for the point source. Also, we show that to achieve high contrast with a point source, tuning the source size and its distance to the element is crucial.We furthermore indicate and explore the possibility of realizing highly complex light patterns by using a periodic transmission element. These patterns can have more spots in the far field than the number of diffraction orders of the periodic element. We predict that the ultimate image contrast is smaller for a point source compared to a plane wave. Our simulations confirm that the smallest achievable spot size in the image is imposed by diffraction regardless of the imaging regime. Our research can be applied to similar domains e.g. quantum systems.

Bounce resonance diffusion coefficients for spatially confined waves

AbstractTheoretical bounce resonance diffusion coefficients from interactions between electrons and spatially confined waves are derived and validated. Roberts and Schulz bounce resonance diffusion coefficients assume waves to be present on the whole bounce trajectory of particles; therefore, they are not directly applicable to waves that have a finite spatial extent. We theoretically derive and numerically validate a new set of bounce resonance diffusion coefficients for spatially confined waves. We apply our analysis to magnetosonic waves, which are confined to equatorial regions, using a previously published magnetosonic wave model. We find that the bounce resonance diffusion coefficients are comparable to the gyroresonance diffusion coefficients. We conclude that bounce resonance diffusion with magnetosonic waves might play an important role in relativistic electron dynamics.

Spatial arrangement of décollements as a control on the development of thrust faults

We used two-dimensional finite element models to explore different configurations of weak layers in undeformed sedimentary sequences to investigate the occurrence of three characteristic types of thrust configurations: ramp-flat; imbricate; and duplex. In our models, we embedded two low-friction weak layers with a finite spatial extent in a sequence of stronger rock. These two weak layers were initially horizontal, were separated vertically by 1 km, and were arranged in three different relative positions to each other. When the models were deformed and these weak layers developed into décollements, they interacted to produce one of the three types of thrust faults as a function of their initial configurations. When the tips of weak layers were separated by a large gap (>10 km), only the lower-level décollement became active, producing imbricate thrusts. When the two weak layers overlapped for a large distance (>10 km), they simultaneously became active décollements, producing duplexes in the overlapped zone. When the gap or overlap was small (<5 km), the two weak layers also simultaneously became active décollements but their tips linked up to form a ramp-flat geometry. These results suggest that thrust geometry is highly sensitive to the initial arrangement of décollements.