Anisotropic Dilation Research Articles

A Molecular‐Scale Origin of Shear Thinning and Brittle Failure of Silicate Melt

AbstractShear thinning and brittle failure of silicate melt control the dynamics of volcanic eruptions, but their molecular‐scale origin is still unclear. Here, we conducted tension and compression experiments on silicate melts, using time‐resolved X‐ray diffraction. Our experiments revealed that the intermediate‐range ordering of silicate structures, that is, the ring size formed by the SiO4 tetrahedra, demonstrated elastic and anisotropic dilation under tension and shrinkage under compression in the non‐Newtonian regime. In contrast, there were no significant changes in short‐range ordering, such as Si–O and Si–Si distances. Based on these findings, we inferred that shear thinning observed under high stress originates from the formation of anisotropically deformed large and small rings in silicate structures that are energetically unfavorable and unstable. Brittle failure occurred under high‐stress conditions, in both tension and compression. We propose a stress criterion as a necessary and sufficient condition for magma failure, rather than a strain rate criterion.

Lifshitz symmetry: Lie algebras, spacetimes and particles

We study and classify Lie algebras, homogeneous spacetimes and coadjoint orbits (“particles”) of Lie groups generated by spatial rotations, temporal and spatial translations and an additional scalar generator. As a first step we classify Lie algebras of this type in arbitrary dimension. Among them is the prototypical Lifshitz algebra, which motivates this work and the name “Lifshitz Lie algebras”. We classify homogeneous spacetimes of Lifshitz Lie groups. Depending on the interpretation of the additional scalar generator, these spacetimes fall into three classes:1. (d+2)-dimensional Lifshitz spacetimes which have one additional holographic direction;2. (d+1)-dimensional Lifshitz-Weyl spacetimes which can be seen as the boundary geometry of the spacetimes in (1) and where the scalar generator is interpreted as an anisotropic dilation;3. and (d+1)-dimensional aristotelian spacetimes with one scalar charge, including exotic fracton-like symmetries that generalise multipole algebras.We also classify the possible central extensions of Lifshitz Lie algebras and we discuss the homogeneous symplectic manifolds of Lifshitz Lie groups in terms of coadjoint orbits.

Molecular-scale structural changes of silicate melts under tension revealed by time-resolved X-ray diffraction

The non-Newtonian behavior of silicate melts influences magma flow dynamics in a volcanic conduit. Shear thinning causes a reduction in viscosity and brittle failure induces magma fragmentation, resulting in explosive eruptions that release magma fragments into the surface with volcanic gases. The conditions under which they occur have been investigated by macroscopic rheological experiments; however, the understanding of the molecular-scale origin of shear thinning and brittle failure of silicate melts remains poor, partially because of the experimental difficulty of in situ investigations of molecular-scale melt structures under deformation. In this study, we performed tension experiments for silicate melts at temperatures of 760–840 °C and investigated the melt structure forming intermediate-range ordering using time-resolved X-ray diffraction. Our experiments demonstrate that the contribution of anisotropic elastic deformation to molecular-scale strain increases with increasing stress. The mechanical data for stress relaxation indicate that the relaxation timescale decreases with an increase in stress, implying viscosity reduction with an increase in stress. Based on this, we infer that when the stress is large, the molecular-scale structure elastically dilates in the direction of the deformation under tension, causing a decrease in melt viscosity, and the melt may cause macroscopic failure through local anisotropic dilation and the resultant cavitation. This process seems to depend on experimental geometry, such as tension, compression, and torsion; hence, the relationship between experimental geometry, molecular-scale structure, and non-Newtonian behavior must be further investigated in future studies.

Imaging Nanometer Phonon Softening at Crystal Surface Steps with 4D Ultrafast Electron Microscopy.

Step edges are an important and prevalent topological feature that influence catalytic, electronic, vibrational, and structural properties arising from modulation of atomic-scale force fields due to edge-atom relaxation. Direct probing of ultrafast atomic-to-nanoscale lattice dynamics at individual steps poses a particularly significant challenge owing to demanding spatiotemporal resolution requirements. Here, we achieve such resolutions with femtosecond 4D ultrafast electron microscopy and directly image nanometer-variant softening of photoexcited phonons at individual surface steps. We find large degrees of softening precisely at the step position, with a thickness-dependent, strain-induced frequency modulation extending tens of nanometers laterally from the atomic-scale discontinuity. The effect originates from anisotropic bond dilation and photoinduced incoherent atomic displacements delineated by abrupt molecular-layer cessation. The magnitude and spatiotemporal extent of softening is quantitatively described with a finite-element transient-deformation model. The high spatiotemporal resolutions demonstrated here enable uncovering of new insights into atomic-scale structure-function relationships of highly defect-sensitive, functional materials.

The one-way speed of light and the Milne universe

Abstract In Einstein’s special theory of relativity, all observers measure the speed of light, c, to be the same. However, this refers to the round-trip speed, where a clock at the origin times the outward and return trip of light reflecting off a distant mirror. Measuring the one-way speed of light is fraught with issues of clock synchronisation, and, as long as the average speed of light remains c, the speeds on the outward and return legs could be different. One objection to this anisotropic speed of light is that views of the distant universe would be different in different directions, especially with regard to the ages of observed objects and the smoothness of the Cosmic Microwave Background. In this paper, we explore this in the Milne universe, the limiting case of a Friedmann–Robertson–Walker universe containing no matter, radiation, or dark energy. Given that this universe is empty, it can be mapped onto flat Minkowski space-time and so can be explored in terms of the one-way speed of light. The conclusion is that the presence of an anisotropic speed of light leads to anisotropic time dilation effects, and hence observers in the Milne universe would be presented with an isotropic view of the distant cosmos.

A new molecular characterization of diagonal anisotropic Musielak-Orlicz Hardy spaces

Let D:=diag(λ1,⋯,λn), where {λi}i=1n⊂C, be a diagonal anisotropic dilation on Rn with min1≤i≤n⁡|λi|>1 and let φ:Rn×[0,∞)→[0,∞) be an anisotropic growth function. In this article, the authors introduce the anisotropic Musielak-Orlicz Hardy space HDφ(Rn) via the grand maximal function and establish its molecular characterization via the atomic characterization of HDφ(Rn). As an application, the authors obtain the boundedness of a new class of general integral anisotropic Calderón-Zygmund operators from HDφ(Rn) to Lφ(Rn) or from HDφ(Rn) to itself.

Boundedness of singular integrals on the flag Hardy spaces on Heisenberg group

We prove that the classical one-parameter convolution singular integrals on the Heisenberg group are bounded on multiparameter flag Hardy spaces, which satisfy the ‘intermediate’ dilation between the one-parameter anisotropic dilation and the product dilation on Cn×R implicitly.

Phase stability, swelling, microstructure and strength of Ti3SiC2-TiC ceramics after low dose neutron irradiation

Mn+1AXn (MAX) phase Ti3SiC2 materials were neutron irradiated at ∼400, ∼630, and 700 °C to a fluence of ∼2 × 1025 n/m2 (E > 0.1 MeV). After irradiation at ∼400 °C, anisotropic c-axis dilation of ∼1.5% was observed. Room temperature strength was reduced from 445 ± 29 MPa to 315 ± 33 MPa and the fracture surfaces showed flat facets and transgranular cracks instead of typical kink-band deformation and bridging ligaments. XRD phase analysis indicated an increase of 10–15 wt% TiC. After irradiation at ∼700 °C there were no lattice parameter changes, ∼5 wt% decomposition to TiC occurred, and strength was 391 ± 71 MPa and 378 ± 31 MPa. The fracture surfaces indicated kink-band based deformation but with lesser extent of delamination than as-received samples. Ti3SiC2 appears to be radiation tolerant at ∼400 °C, and increasingly radiation resistant at ∼630–700 °C, but a higher temperature may be necessary for full recovery.

Microlocal analysis of edge flatness through directional multiscale representations

Edges and surface boundaries are often the most relevant features in images and multidimensional data. It is well known that multiscale methods including wavelets and their more sophisticated multidimensional siblings offer a powerful tool for the analysis and detection of such sets. Among such methods, the continuous shearlet transform has been especially successful. This method combines anisotropic scaling and directional sensitivity controlled by shear transformations in order to precisely identify not only the location of edges and boundary points but also edge orientation and corner points. In this paper, we show that this framework can be made even more flexible by controlling the scaling parameter of the anisotropic dilation matrix and considering non-parabolic scaling. We prove that, using `higher-than-parabolic' scaling, the modified shearlet transform is also able to estimate the degree of local flatness of an edge or surface boundary, providing more detailed information about the geometry of edge and boundary points.

3He retention and structural evolution in erbium tritides: Phase and aging effects

Effects of phase changes on 3He release/retention and crystal lattice evolution during aging of erbium (Er) tritide films were investigated using X-ray diffraction. The contents of α phase and γ phase in the Er tritide films showed significant different effects on 3He release/retention. The initial tritium stoichiometry or excess tritium atoms accommodated in the octahedral sites and the microstructure (i.e., the texture and Er2O3 oxide inclusions) played an important role for the 3He release and the evolution of 3He bubbles in the β phase Er tritide films. In the β+γ region, evolution of 3He in the β phase was apparently influenced by the γ phase, which could result in a strongly anisotropic lattice dilation and an earlier inflection point of the expansion rate of (111) lattice parameter. A preferred occupation of 3He in basal plane of the hexagonal γ phase and the lattice expansion along the hexagonal direction were identified.

3D Alfvén wave behaviour about proper and improper magnetic null points

Context: MHD waves and magnetic null points are both prevalent in many astrophysical plasmas, including the solar atmosphere. Interaction between waves and null points has been implicated as a possible mechanism for localised heating events. Aims: Here we investigate the transient behaviour of the Alfven wave about fully 3D proper and improper 3D magnetic null points. Previously, the behaviour of fast magnetoacoustic waves at null points in 3D, cold MHD was considered by Thurgood & McLaughlin (Astronomy & Astrophysics, 2012, 545, A9). Methods: We introduce an Alfven wave into the vicinity of both proper and improper null points by numerically solving the ideal, $\beta=0$ MHD equations using the LARE3D code. A magnetic fieldline and flux-based coordinate system permits the isolation of resulting wave-modes and the analysis of their interaction. Results: We find that the Alfven wave propagates throughout the region and accumulates near the fan-plane, causing current build up. For different values of null point eccentricity, the qualitative behaviour changes only by the imposition of anisotropic pulse dilation, due to the differing rates at which fieldlines diverge from the spine. For all eccentricities, we find that the fast and Alfven waves are linearly decoupled. During the driving phase, an independently propagating fast wave is nonlinearly generated due to the ponderomotive force. Subsequently, no further excitation of fast waves occurs. Conclusions: We find that the key aspects of the theory of Alfv\'en waves about 2D null points extends intuitively to the fully 3D case; i.e. the wave propagates along fieldlines and thus accumulates at predictable parts of the topology. We also highlight that unlike in the 2D case, in 3D Alfven-wave pulses are always toroidal and thus any aspects of 2D Alfven-wave-null models that are pulse-geometry specific must be reconsidered in 3D.

On the Representation of Functions with Gaussian Wave Packets

We introduce Gaussian wave packets in pursuit of representations of functions, in which the representation is invariant under translation, modulation, scale, rotation and anisotropic dilation. Properties of both continuous and discrete representations are discussed. For the discrete (two-dimensional) case, we develop fast algorithms for the application of the analysis and synthesis operators. A main objective for using Gaussian wave packets is to obtain sparse approximations of functions. However, due to the many invariance properties, the representations will have a high degree of redundancy. Therefore, we also introduce sparse methods for highly redundant representations, that employ some of the analytic properties of Gaussian wave packet for gaining computational efficiency.

Simulation of anisotropic dilation behaviour of layered and banded steel samples during phase changes

We consider anisotropic distortions due to solid–solid phase transformations during heat treatment of a layered or banded material which exhibits transformation-induced plasticity. These anisotropic macroscopic effects are due to the local microstructure orientation on a mesoscopic scale. We present numerical simulations for different types of microstructure and their effect on macroscopically observable deformations.

Size Change due to Anisotropic Dilation Behaviour of a Low Alloy SAE 5120 Steel

A conventional hot rolled, low alloy carburizing steel (C: 0.21 wt.‐%; Cr: 1.08 wt.%; Mn: 1.36 wt.%) has been investigated in terms of inhomogeneous phase transformations and anisotropic size changes during heating to austenitizing temperature and during slow cooling from austenitizing temperature to room temperature. A detailed study was executed on dilatometer specimens. The results were compared with the size changes of shafts with similar heat treatment. Ferrite nucleated first at selected chain‐like positions and a pronounced ferrite/pearlite rodlike structure was formed. After reaustenitizing the rodlike structure appeared exactly at the same position. At intermediate transformation stages broad regions were still untransformed while other regions had an advanced transformation state. Dilatometer specimens with different orientations to the former rolling direction of the bar had different changes in length, which indicates an anisotropic size change. Cylindrical shafts showed a similar macroscopic size change like the small dilatometer specimens. For the dilatometer specimens as well as for the shafts the absolute valuese of the size change depended on the initial microstructure.

Roche lobe shapes for testing MOND-like modified gravities

Dark Matter (DM) theories and mass-tracing-light theories like MOND are by construction nearly degenerate on galactic scales, but not when it comes to the predicted shapes of Roche Lobes of a two-body system (e.g., a globular cluster orbiting a host galaxy). We show that the flattening of the Roche lobe is sensitive to the function mu(g) in modification of the law of gravity. We generalise the analytical results obtained in the deep-MOND limit by Zhao (2005), and consider a binary in the framework of a MOND-like gravity modification function mu(g) or a general non-Keplerian gravity g proportional to R-zeta. We give analytical expressions for the inner Lagrange point and Robe lobe axis ratios. The Roche lobe volume is proven to scale linearly with the true mass ratio, which applies to any mu(g), hence mass-tracing light models would overpredict the Roche lobe of a DM-poor globular cluster in a DM-rich host galaxy, and underpredict the size of a DM-richer dwarf satellite. The lobes are squashed with the flattening similar to 0.4 in the strong gravity and similar to 0.6 in the weak gravity; a precise measurement of the flattening could be used to verify the anisotropic dilation effect which is generic to MOND-like gravity. We generalise these results for extended mass distribution, and compare predicted Roche radii with limiting radii of observed globular clusters and dwarf galaxy satellites.

Roche lobe sizes in deep-MOND gravity

MOdified Newtonian Dynamics (MOND) is evolving from an empirical to a decent theory respect- ing fundamental physics after Bekenstein (2004) showed that lensing and Hubble expansion can be modeled rigourously in a Modified Relativity. The degeneracy of MOND with Dark Matter can be broken if we examine the non-linear MONDian Poisson's equation in detail. Here we study the effect of tides for a binary stellar system or a baryonic satellite-host galaxy system. We show that the Roche lobe is more squashed than the Newtonian case due to the anisotropic dilation effect in deep-MOND. We prove analytically that the Roche lobe volume scales linearly with the true baryonic mass ratio in both Newtonian and deep-MOND regimes, insensitive to the modification to the inertia mass. Hence accurate Roche radii of satellites can break the degeneracy of MOND and dark matter theory. Globular clusters and dwarf galaxies of comparable luminosities and distances show a factor of ten scatter in limiting radii; this is difficult to explain in any mass-tracing-light universe. The results here are generalizable to the intermediate MOND regime for a wide class of gravity modification function µ(g) (Zhao and Tian, astro-ph/0511754).

Effects of milling-induced disorder on the lattice parameters and magnetic properties of hematite

A ball-milling treatment in air for 30 min is enough to reduce anhydrous bulk hematite (α-Fe 2O 3) grains to nanometric sizes. For milling times, t m, of 15, 30 min, 1 and 2 h, the crystals suffer an anisotropic lattice dilation, which is more pronounced for the smaller average grain sizes attained. Mössbauer and susceptibility results show that the process alters the effective Morin temperatures, T M. The transition occurs less sharply than for the non-milled material and spreads over a maximum extent of 50 K for t m=30 min. The susceptibility data indicate that the T M for the fraction of material undergoes the transition shifts toward values not lower than 235 K. For t m=10 h the transition is suppressed down to 12 K. Our results do not allow distinguishing bulk from surface regions of the grains. In addition, the disorder brought about by the milling reduces the magnetic response in the weak ferromagnetic state of α-Fe 2O 3. The modification of T M seems to depend mainly on the anisotropic dilation of the unit cell that affects the whole grain and it is related to the nanometric grain sizes achieved.

How to describe pure form and how to measure differences in shapes using shape numbers

The shape number of a curve is derived for two-dimensional non-intersecting closed curves that are the boundary of simply connected regions. This description is independent of their size, orientation and position, but it depends on their shape. Each curve carries “within it” its own shape number. The order of the shape number indicates the precision with which that number describes the shape of the curve. For a curve, the order of its shape number is the length of the perimeter of a ‘discrete shape’ (a closed curve formed by vertical and horizontal segments, all of equal length) closely corresponding to the curve. A procedure is given that deduces, without table look-up, string matching or correlations, the shape number of any order for an arbitrary curve. To find out how close in shape two curves are, the degree of similarity between them is introduced; dissimilar regions will have a low degree of similarity, while analogous shapes will have a high degree of similarity. Informally speaking, the degree of similarity between the shapes of two curves tells how deep it is necessary to descend into a list of shapes, before being able to differentiate between the shape of those two curves. Again, a procedure is given to compute it, without need for such list or grammatical parsing or least square curve or area fitting. The degree of similarity maps the universe of curves into a tree or hierarchy of shapes. The distance between the shapes of any two curves, defined as the inverse of their degree of similarity, is found to be an ultradistance over this tree. The shape number is a description that changes with skewing, anisotropic dilation and mirror images, as the intuitive psychological concept of “shape” demands. Nevertheless, at the end of the paper a related Theory “ B” of shapes is introduced that allows anisotropic changes of scale, thus permitting for instance a rectangle and a square to have the same B shape. These definitions and procedures may facilitate a quantitative study of shape.