Amplitude equations for systems with long-range interactions

We derive amplitude equations for interface dynamics in pattern forming systems with long-range interactions. The basic condition for the applicability of the method developed here is that the bulk equations are linear and solvable by integral transforms. We arrive at the interface equation via long-wave asymptotics. As an example, we treat the Grinfeld instability, and we also give a result for the Saffman-Taylor instability. It turns out that the long-range interaction survives the long-wave limit and shows up in the final equation as a nonlocal and nonlinear term, a feature that to our knowledge is not shared by any other known long-wave equation. The form of this particular equation will then allow us to draw conclusions regarding the universal dynamics of systems in which nonlocal effects persist at the level of the amplitude description.Comment: LaTeX source, 12 pages, 4 figures, accepted for Physical Review

Phase Field Modeling of Fast Crack Propagation

We present a continuum theory which predicts the steady state propagation of cracks. The theory overcomes the usual problem of a finite time cusp singularity of the Grinfeld instability by the inclusion of elastodynamic effects which restore selection of the steady state tip radius and velocity. We developed a phase field model for elastically induced phase transitions; in the limit of small or vanishing elastic coefficients in the new phase, fracture can be studied. The simulations confirm analytical predictions for fast crack propagation.Comment: 5 pages, 11 figure

Fracture in Mode I using a Conserved Phase-Field Model

We present a continuum phase-field model of crack propagation. It includes a phase-field that is proportional to the mass density and a displacement field that is governed by linear elastic theory. Generic macroscopic crack growth laws emerge naturally from this model. In contrast to classical continuum fracture mechanics simulations, our model avoids numerical front tracking. The added phase-field smoothes the sharp interface, enabling us to use equations of motion for the material (grounded in basic physical principles) rather than for the interface (which often are deduced from complicated theories or empirical observations). The interface dynamics thus emerges naturally. In this paper, we look at stationary solutions of the model, mode I fracture, and also discuss numerical issues. We find that the Griffith's threshold underestimates the critical value at which our system fractures due to long wavelength modes excited by the fracture process.Comment: 10 pages, 5 figures (eps). Added 2 figures and some text. Removed one section (and a figure). To be published in PR

Influence of uniaxial stress on the lamellar spacing of eutectics

Directional solidification of lamellar eutectic structures submitted to uniaxial stress is investigated. In the spirit of an approximation first used by Jackson and Hunt, we calculate the stress tensor for a two-dimensional crystal with triangular surface, using a Fourier expansion of the Airy function. crystal with triangular surface in contact with its melt, given that a uniaxial external stress is applied. The effect of the resulting change in chemical potential is introduced into the standard model for directional solidification of a lamellar eutectic. This calculation is motivated by an observation, made recently [I. Cantat, K. Kassner, C. Misbah, and H. M\"uller-Krumbhaar, Phys. Rev. E, in press] that the thermal gradient produces similar effects as a strong gravitational field in the case of dilute-alloy solidification. Therefore, the coupling between the Grinfeld and the Mullins-Sekerka instabilities becomes strong, as the critical wavelength of the former instability gets reduced to a value close to that of the latter. Analogously, in the case of eutectics, the characteristic length scale of the Grinfeld instability should be reduced to a size not extremely far from typical lamellar spacings. In a Jackson-Hunt like approach we average the undercooling, including the stress term, over a pair of lamellae. Following Jackson and Hunt, we assume the selected wavelength to be determined by the minimum undercooling criterion and compute its shift due to the external stress. we realize the shifting of the wavelength by the application of external stress. In addition, we find that in general the volume fraction of the two solid phases is changed by uniaxial stress. Implications for experiments on eutectics are discussed.Comment: 8 pages RevTex, 6 included ps-figures, accepted for Phys. Rev.

Pattern formation in directional solidification under shear flow. I: Linear stability analysis and basic patterns

An asymptotic interface equation for directional solidification near the absolute stabiliy limit is extended by a nonlocal term describing a shear flow parallel to the interface. In the long-wave limit considered, the flow acts destabilizing on a planar interface. Moreover, linear stability analysis suggests that the morphology diagram is modified by the flow near the onset of the Mullins-Sekerka instability. Via numerical analysis, the bifurcation structure of the system is shown to change. Besides the known hexagonal cells, structures consisting of stripes arise. Due to its symmetry-breaking properties, the flow term induces a lateral drift of the whole pattern, once the instability has become active. The drift velocity is measured numerically and described analytically in the framework of a linear analysis. At large flow strength, the linear description breaks down, which is accompanied by a transition to flow-dominated morphologies, described in a companion paper. Small and intermediate flows lead to increased order in the lattice structure of the pattern, facilitating the elimination of defects. Locally oscillating structures appear closer to the instability threshold with flow than without.Comment: 20 pages, Latex, accepted for Physical Review

Language Models As or For Knowledge Bases

Pre-trained language models (LMs) have recently gained attention for their potential as an alternative to (or proxy for) explicit knowledge bases (KBs). In this position paper, we examine this hypothesis, identify strengths and limitations of both LMs and KBs, and discuss the complementary nature of the two paradigms. In particular, we offer qualitative arguments that latent LMs are not suitable as a substitute for explicit KBs, but could play a major role for augmenting and curating KBs

A Supercooled Spin Liquid State in the Frustrated Pyrochlore Dy2Ti2O7

A "supercooled" liquid develops when a fluid does not crystallize upon cooling below its ordering temperature. Instead, the microscopic relaxation times diverge so rapidly that, upon further cooling, equilibration eventually becomes impossible and glass formation occurs. Classic supercooled liquids exhibit specific identifiers including microscopic relaxation times diverging on a Vogel-Tammann-Fulcher (VTF) trajectory, a Havriliak-Negami (HN) form for the dielectric function, and a general Kohlrausch-Williams-Watts (KWW) form for time-domain relaxation. Recently, the pyrochlore Dy2Ti2O7 has become of interest because its frustrated magnetic interactions may, in theory, lead to highly exotic magnetic fluids. However, its true magnetic state at low temperatures has proven very difficult to identify unambiguously. Here we introduce high-precision, boundary-free magnetization transport techniques based upon toroidal geometries and gain a fundamentally new understanding of the time- and frequency-dependent magnetization dynamics of Dy2Ti2O7. We demonstrate a virtually universal HN form for the magnetic susceptibility, a general KWW form for the real-time magnetic relaxation, and a divergence of the microscopic magnetic relaxation rates with precisely the VTF trajectory. Low temperature Dy2Ti2O7 therefore exhibits the characteristics of a supercooled magnetic liquid; the consequent implication is that this translationally invariant lattice of strongly correlated spins is evolving towards an unprecedented magnetic glass state, perhaps due to many-body localization of spin.Comment: Version 2 updates: added legend for data in Figures 4A and 4B; corrected equation reference in caption for Figure 4

MRI-based cerebrovascular reactivity using transfer function analysis reveals temporal group differences between patients with sickle cell disease and healthy controls

AbstractObjectivesCerebrovascular reactivity (CVR) measures the ability of cerebral blood vessels to change their diameter and, hence, their capacity to regulate regional blood flow in the brain. High resolution quantitative maps of CVR can be produced using blood-oxygen level-dependent (BOLD) magnetic resonance imaging (MRI) in combination with a carbon dioxide stimulus, and these maps have become a useful tool in the clinical evaluation of cerebrovascular disorders. However, conventional CVR analysis does not fully characterize the BOLD response to a stimulus as certain regions of the brain are slower to react to the stimulus than others, especially in disease. Transfer function analysis (TFA) is an alternative technique that can account for dynamic temporal relations between signals and has recently been adapted for CVR computation. We investigated the application of TFA in data on children with sickle cell disease (SCD) and healthy controls, and compared them to results derived from conventional CVR analysis.Materials and methodsData from 62 pediatric patients with SCD and 34 age-matched healthy controls were processed using conventional CVR analysis and TFA. BOLD data were acquired on a 3Tesla MRI scanner while a carbon dioxide stimulus was quantified by sampling the end-tidal partial pressures of each exhaled breath. In addition, T1 weighted structural imaging was performed to identify grey and white matter regions for analysis. The TFA method generated maps representing both the relative magnitude change of the BOLD signal in response to the stimulus (Gain), as well as the BOLD signal speed of response (Phase) for each subject. These were compared to CVR maps calculated from conventional analysis. The effect of applying TFA on data from SCD patients versus controls was also examined.ResultsThe Gain measures derived from TFA were significantly higher than CVR values based on conventional analysis in both SCD patients and healthy controls, but the difference was greater in the SCD data. Moreover, while these differences were uniform across the grey and white matter regions of controls, they were greater in white matter than grey matter in the SCD group. Phase was also shown to be significantly correlated with the amount that TFA increases CVR estimates in both the grey and white matter.ConclusionsWe demonstrated that conventional CVR analysis underestimates vessel reactivity and this effect is more prominent in patients with SCD. By using TFA, the resulting Gain and Phase measures more accurately characterize the BOLD response as it accounts for the temporal dynamics responsible for the CVR underestimation. We suggest that the additional information offered through TFA can provide insight into the mechanisms underlying CVR compromise in cerebrovascular diseases

Quantum phase transition of Ising-coupled Kondo impurities

We investigate a model of two Kondo impurities coupled via an Ising interaction. Exploiting the mapping to a generalized single-impurity Anderson model, we establish that the model has a singlet and a (pseudospin) doublet phase separated by a Kosterlitz-Thouless quantum phase transition. Based on a strong-coupling analysis and renormalization group arguments, we show that at this transition the conductance G through the system either displays a zero-bias anomaly, G ~ |V|^{-2(\sqrt{2}-1)}, or takes a universal value, G = e^2/(\pi\hbar) cos^2[\pi/(2\sqrt{2})], depending on the experimental setup. Close to the Toulouse point of the individual Kondo impurities, the strong-coupling analysis allows to obtain the location of the phase boundary analytically. For general model parameters, we determine the phase diagram and investigate the thermodynamics using numerical renormalization group calculations. In the singlet phase close to the quantum phase transtion, the entropy is quenched in two steps: first the two Ising-coupled spins form a magnetic mini-domain which is, in a second step, screened by a Kondoesque collective resonance in an effective solitonic Fermi sea. In addition, we present a flow equation analysis which provides a different mapping of the two-impurity model to a generalized single-impurity Anderson model in terms of fully renormalized couplings, which is applicable for the whole range of model parameters.Comment: 24 pages, 12 figs; (v2) minor changes, flow equation section extende

Integrated atomic quantum technologies in demanding environments: Development and qualification of miniaturized optical setups and integration technologies for UHV and space operation

Employing compact quantum sensors in field or in space (e.g., small satellites) implies demanding requirements on components and integration technologies. Within our work on integrated sensors, we develop miniaturized, ultra-stable optical setups for optical cooling and trapping of cold atomic gases. Besides challenging demands on alignment precision, and thermo-mechanical durability, we specifically address ultra-high vacuum (UHV) compatibility of our integration technologies and optical components. A prototype design of an UHV-compatible, crossed beam optical dipole trap setup and its application within a cold atomic quantum sensor is described. First qualification efforts on adhesive micro-integration technologies are presented. These tests are conducted in application-relevant geometries and material combinations common for micro-integrated optical setups. Adhesive aging will be investigated by thermal cycling or gamma radiation exposure. For vacuum compatibility testing, a versatile UHV testing system is currently being set up, enabling residual gas analysis and measurement of total gas rates down to 5•10-10mbar l/s at a base pressure of 10-11 mbar, exceeding the common ASTM E595 test