Thiele Approach Research Articles

Emergent Magnetic Field and Nonzero Gyrovector of the Toroidal Magnetic Hopfion

Magnetic hopfions are localized magnetic solitons with a nonzero 3D topological charge (Hopf index). Herein, an analytical calculation of the magnetic hopfion gyrovector is presented and it is shown that it does not vanish even in an infinite sample. The calculation method is based on the concept of the emergent magnetic field. The particular case of the simplest nontrivial toroidal hopfion with the Hopf index in the cylindrical magnetic dot is considered and dependencies of the gyrovector components on the dot sizes are calculated. Nonzero hopfion gyrovector is important in any description of the hopfion dynamics within the collective coordinate Thiele's approach.

Design, construction and commissioning of a high-flow radon removal system for XENONnT

A high-flow radon removal system based on cryogenic distillation was developed and constructed to reduce radon-induced backgrounds in liquid xenon detectors for rare event searches such as XENONnT. A continuous purification of the XENONnT liquid xenon inventory of 8.4 tonnes at process flows up to 71 kg/h (200 slpm) is required to achieve a radon reduction by a factor larger than two for radon sources inside the detector. To reach such high flows, the distillation column’s design features liquid xenon inlet and outlets along with novel custom-made bath-type heat exchangers with high liquefaction capabilities. The distillation process was designed using a modification of the McCabe–Thiele approach without a bottom product extraction. The thermodynamic concept is based on a Clausius–Rankine cooling cycle with phase-changing medium, in this case the xenon itself. To drastically reduce the external cooling power requirements, an energy efficient heat pump concept was developed applying a custom-made four cylinder magnetically-coupled piston pump as compressor. The distillation system was operated at thermodynamically stable conditions at a process flow of ({91pm 2}),mathrm{kg/h} ((258pm 6) slpm), 30% over design. With this flow, a activity concentration <1,upmu Bq/kg is expected inside the XENONnT detector given the measured radon source distribution.

Depinning phase transition of antiferromagnetic skyrmions with quenched disorder

Antiferromagnetic skyrmions are considered to be promising information carriers due to their attractive properties. Therefore, the pinning phenomenon of antiferromagnetic skyrmions is of great significance. With the Landau-Lifshitz-Gilbert equation, we simulate the nonstationary dynamic behaviors of skyrmions driven by currents in a chiral antiferromagnetic thin film with quenched disorder. Based on the dynamic scaling forms, the critical current and static and dynamic critical exponents of the depinning phase transition are accurately determined. A theoretical analysis using Thiele's approach is presented in comparison with the numerical simulation. Unlike the ferromagnetic skyrmions, the critical current of the antiferromagnetic skyrmions is very sensitive to a small nonadiabatic coefficient. This is important for manipulating antiferromagnetic skyrmions and designing novel information processing devices.

The skyrmion bags in an anisotropy gradient

Skyrmion bags as spin textures with arbitrary topological charge are expected to be the carriers in racetrack memory. Here, we theoretically and numerically investigated the dynamics of skyrmion bags in an anisotropy gradient. It is found that, without the boundary potential, the dynamics of skyrmion bags are dependent on the spin textures, and the velocity of skyrmionium with Q = 0 is faster than other skyrmion bags. However, when the skyrmion bags move along the boundary, the velocities of all skyrmion bags with different Q are same. In addition, we theoretically derived the dynamics of skyrmion bags in the two cases using the Thiele approach and discussed the scope of Thiele equation. Within a certain range, the simulation results are in good agreement with the analytically calculated results. Our findings provide an alternative way to manipulate the racetrack memory based on the skyrmion bags.

Skyrmion Dynamics in the Presence of Deformation

The nonlinear dynamics of current-driven skyrmions are essential for designing skyrmion-based spintronic devices. However, Thiele's approach uses a rigid-body assumption that is not suitable here, as skyrmions may change shape at high speeds. This study extends Thiele's equation by including the radial and tangential force components. With this approach, one may depict the inner structure of a current-driven skyrmion and propose a way to suppress deformation with an in-plane magnetic field. This extended analytic formulation may help to describe the nonlinear dynamics of other spin textures as well, and to promote applications based on such dynamics.

Signal detection based on the chaotic motion of an antiferromagnetic domain wall

The antiferromagnetic domain wall dynamics is currently a hot topic in mesoscopic magnetic systems. In this work, it is found that, based on the Thiele approach, the motion of an antiferromagnetic domain wall is described by the Duffing equation. Numerical simulations demonstrate that the antiferromagnetic domain wall can be used as a Duffing oscillator, and the transition between the periodic and chaotic motion can be used to detect the periodic signal in the presence of the white noise. Furthermore, we calculate the bifurcation diagram and Lyapunov exponents to study the chaotic behavior of an antiferromagnetic domain wall. The numerical simulations are in good agreement with the analytical solutions. Our results may be useful for building spintronic detection devices based on antiferromagnetic domain walls.

Dynamics of antiferromagnetic skyrmions in the absence or presence of pinning defects

A theoretical study on the dynamics of an antiferromagnetic (AFM) skyrmion is indispensable for revealing the underlying physics and understanding the numerical and experimental observations. In this work, we present a reliable theoretical treatment of the spin current induced motion of an AFM skyrmion in the absence and presence of pinning defect. For an ideal AFM system free of defect, the skyrmion motion velocity as a function of the intrinsic parameters can be derived, based on the concept that the skyrmion profile agrees well with the 360 domain wall formula, leading to an explicit description of the skyrmion dynamics. However, for an AFM lattice containing a defect, the skyrmion can be pinned and the depinning field as a function of damping constant and pinning strength can be described by the Thiele approach. It is revealed that the depinning behavior can be remarkably influenced by the time dependent oscillation of the skyrmion trajectory. The present theory provides a comprehensive scenario for manipulating the dynamics of AFM skyrmion, informative for future spintronic applications based on antiferromagnets.

Theoretical Analysis of the Change in Ion Exchange Selectivity in the Complex Displacement Chromatography Systems

The ion exchange selectivity of complex displacement chromatography (CDC) is analyzed. It is found that the separation factors determined by other means of complex chromatography, frontal and elution, are not always interchangeable with CDC. A way of determining the separation factors applied to CDC is proposed. A technique for constructing isotherms for the ion exchange of components to be separated with the simultaneous presence of displacer ions, hydrogen ions, and a sorbed complexone in the system is proposed as well. The change in the selectivity towards different valence elements is considered. For protonated complexes, the complete inversion of selectivity corresponds to the transition of the S-shaped separation isotherm from convex to concave. When protonated and binuclear М2А complexes are simultaneously present in a system, the inversion of selectivity is accompanied by mixed isotherms of variable type with two intersection points with a diagonal. The spreading of the displacement fronts is determined using the McCabe–Thiele approach. The lower part of the displacement front of the second component is spread in the case of a convex isotherm with an S-shaped pattern. For complex isotherms with two maxima, the center of the front is spread, while the lower and upper parts of the front are quite sharp.

Vortex-antivortex dynamics driven by spin-torque in a nanocontact

A spin-polarized current in a nanocontact has been shown to induce the formation of a magnetic vortex at the nanocontact by the Oersted field, and spin-torque drives the vortex core in an elliptical orbit about the nanocontact. For the case of an external in-plane magnetic field in an extended free layer, the magnetization will be uniform far from the nanocontact, implying that vortex formation must be accompanied by the formation of an antivortex. Using the Thiele approach to describe the vortex-antivortex dynamics it is shown that the frequency of gyrotropic motion of the vortex is a function of the nanocontact current which is linear for large vortex-antivortex separations and it becomes nonlinear as the separation is decreased. The equilibrium vortex -antivortex separation can be controlled by the nanocontact current as well as the external magnetic field.

Capturing of a magnetic skyrmion with a hole

Magnetic whirls in chiral magnets, so-called skyrmions, can be manipulated by ultrasmall current densities. Here we study both analytically and numerically the interactions of a single skyrmion in two dimensions with a small hole in the magnetic layer. Results from micromagnetic simulations are in good agreement with effective equations of motion obtained from a generalization of the Thiele approach. Skyrmion-defect interactions are described by an effective potential with both repulsive and attractive components. For small current densities a previously pinned skyrmion stays pinned whereas an unpinned skyrmion moves around the impurities and never gets captured. For higher current densities, j_c1 < j < j_c2, however, single holes are able to capture moving skyrmions. The maximal cross section is proportional to the skyrmion radius and to Sqrt(alpha), where alpha is the Gilbert damping. For j > j_c2 all skyrmions are depinned. Small changes of the magnetic field strongly change the pinning properties, one can even reach a regime without pinning, j_c2=0. We also show that a small density of holes can effectively accelerate the motion of the skyrmion and introduce a Hall effect for the skyrmion.

Influence of temperature and particle size on the single and mixed atmosphere gasification of biomass char with H2O and CO2

The paper focuses on the gasification of biomass chars in H2O, CO2 and their mixtures. The first part is dedicated to the study of the influence of particle size and temperature in single atmosphere gasification experiments. The Thiele approach was successfully applied to assess the extent of diffusional limitations. We also studied the mixed atmosphere gasification of 0.2mm chars at various temperatures and found that the char reactivity is fairly represented by an additive law at relatively low temperatures while it is lower than the sum of the individual contributions for high temperature cases. Similarly, we assessed the effect of particle size for mixed atmosphere experiments and found that an additive law was representative of the experimental reactivities for particle sizes from 0.2 to 13mm. The present work provides useful and worthy information on the char gasification reactivity in conditions close to practical operating ones encountered in biomass gasifiers.

Tunable eigenmodes of coupled magnetic vortex oscillators

We study the magnetization dynamics of coupled vortices in arrays of Permalloy disks via analytical calculations and scanning transmission x-ray microscopy. The Thiele approach is used to derive linear equations of motion of the vortices. Thereby, vortex motions following a nanosecond field pulse are described by a superposition of eigenmodes that depend on the vortex polarizations. Eigenmodes are calculated for a specific polarization pattern of a 3 × 3 vortex array. With magnetic field pulses distinct oscillations are excited and imaged in space and time. The calculated eigenmodes precisely describe the measured oscillations.

Constellations in the Middle Ages

CONSTELLATIONS IN THE MIDDLE AGES Sternbilder des Mittelalters: Der gemalte Himmel zwischen Wissenschaft und Phantasie, Band I: 800-1200. Dieter Blume, Mechthild Haffner and Wolfgang Metzger (Akademie Verlag, Berlin, 2012). Pp. 651+ 403 in two vols. euro298. ISBN 978-3-05-005664-7.In 1898 Georg Thiele published a first, very suggestive of the delineation of celestial in Greek and Roman Antiquity. Thiele's approach was of an art historian, since the process of isolating groups of stars and of naming them involves the projection of figurative into the heavens. However, this nineteenth-century scholar was also familiar with more specialized, mathematical aspects of the of astronomy.More than a century later, a collective of three art historians has extended into the Middle the of celestial conceived primarily as pictorial representations. The first part of their two-part publication, in two volumes, ends with the twelfth century; the second part will cover the period from 1200 through the end of the Middle Ages. The authors relate their work not to Thiele but to Fritz Saxl, who in 1915 published a first catalogue of medieval manuscripts containing astrological and mythological illustrations. And indeed, Sternbilder des Mittelalters is, above all, an extensive catalogue of 68 manuscripts present illustrations of the then usual forty-two (cf., for instance, Hyginus), both isolated and gathered within celestial maps (pp. 179-566). The second volume of Part I is devoted entirely to illustrations.Over the last century, our knowledge of manuscript material has greatly increased and publications dealing with a period of the Middle usually ignored by historians of science have multiplied, especially those concerning time-reckoning (i.e., beyond the work of Charles W. Jones and Amo Borst on the Carolingian period). Relying on an extensive bibliography, Blume, Haffner and Metzger offer, as an introduction, a cultural of the of celestial (pp. 13-176). They systematically contextualize the documents, distinguishing types of manuscripts and textual traditions, as well as general cultural and intellectual environments (monastic and courtly). They focus especially on the computistical manuscripts, comprised of texts deal with time-reckoning and establishing the Church calendar. They also include calendars and more general cosmological expositions. The introduction also attempts to subdivide the period spanning the end of Antiquity to 1200.The authors present their history of the representations of constellations as being, above all, a case study of the usage of in the Middle Ages (p. 66), assigning to these particular three functions: didactical, a bridge to observing nature, and stimulation of viewers' fantasy and imagination (p. 16). Obviously, of the represent a chapter of the of astronomy. However, the authors' understanding of medieval science in general and of astronomy in particular may perplex some readers. Thus, while pushing the beginning of modem science of nature (Naturwissenschaft) as far back as the tenth century, they simultaneously note that the concept 'modem' does not make any sense. For the period of the tenth to the late twelfth century, science is understood to be about questions relating to the calendar, scientific curiosity, and the fascination with images (p. 16). The scope of astronomy is never defined, but appears to be reduced, in their presentation, to the practice of calendar-making and the subject of constellations, occasionally also to representing planets and their movements (the latter in reference to the work of Bruce S. Eastwood). Mathematical aspects are excluded. One might agree, of course, the latter were not a dominant aspect of pre-twelfth-century Latin astronomy. But when it comes to the twelfth century and the reception of Arabic astronomy, the authors' overly general remarks about diagrams are part of geometrical demonstrations are simply inadequate in they are treated as some kind of additions (p. …

Numerical and analytical investigation of the synchronization of dipolarly coupled vortex spin-torque nano-oscillators

We investigate analytically and numerically the synchronization dynamics of dipolarly coupled vortex based Spin-Torque Nano Oscillators with different pillar diameters. We identify the critical interpillar distances on which synchronization occurs as a function of their diameter mismatch. We obtain numerically a phase diagram showing the transition between unsynchronized and synchronized states and compare it to analytical predictions we make using the Thiele approach. Our study demonstrates that for relatively small diameter differences the synchronization dynamics can be described qualitatively using Adler equation. However, when the diameters difference increases significantly, the system becomes strongly non-Adlerian.

Modeling Field-Induced Transformations of Domain Walls in Soft-Magnetic Stripes

Magnetic-field-induced translation of domain walls (DWs) in nanowires and nanostripes is accompanied by oscillatory transformations of the structure of the DW if the field intensity exceeds the Walker breakdown value. Such transformations are analytically described with relevance to soft-magnetic nanostripes, where they are oscillations between a transverse DW, a vortex DW, and an antivortex DW. Two regimes of the stripe thicknesses separated by a critical length of macrospin approximation (of the order of tens of nanometers) are considered. A simple local approach to magnetostatics is used within which the presence of magnetostatic field is included at the stripe edges only via boundary conditions on the DW solutions to the Landau-Lifshitz-Gilbert equation. It enables description of the multi-vortex textures (DWs) in the regime of thick stripes for which validity of the analytical Thiele approach and micromagnetic simulation codes can be questionable because they use different time scales when evaluating magnetostatic and exchange fields. A method of qualitative description of the domain wall transformations in thinner than the critical length stripes is proposed.

Spin torque and critical currents for magnetic vortex nano-oscillator in nanopillars

We calculated the main dynamic parameters of the spin polarized current induced magnetic vortex oscillations in nanopillars, such as the range of current density, where vortex steady oscillations exist, the oscillation frequency and orbit radius. We accounted for both the non-linear vortex frequency and non-linear vortex damping. To describe the vortex excitations by the spin polarized current we used a generalized Thiele approach to motion of the vortex core as a collective coordinate. All the calculation results are represented via the free layer sizes, saturation magnetization, and the Gilbert damping. Predictions of the developed model can be checked experimentally.

Influence of Bubble Evolution on the Effective Kinetics of Heterogeneously Catalyzed Gas/Liquid Reactions. Part I: Reactions with Gaseous Products

AbstractFor heterogeneously catalyzed multiphase reactions the formation of bubbles may have an influence on mass and heat transfer as well as on the effective reaction rate. This first of two contributions deals with the Ni‐catalyzed decomposition of H2O2, which was used as a model system for an (almost) isothermal reaction with a gaseous product. (In part II the strongly exothermic hydrogenation of hexene will be analyzed, where gas/vapor bubbles may be generated by overheating of the catalyst.) The discharge of O2 bubbles formed by decomposition of H2O2 enhances the external mass and heat transfer up to one order of magnitude. This is in analogy to the well‐known phenomena during nucleate boiling. The experiments and theoretical considerations also show that the internal mass transfer depends on the intensity of the reaction and thus on the H2O2 concentration, which is in contradiction to the classical Thiele approach. This discrepancy could be explained by a modified model that takes the formation of bubbles into account.

Vortex oscillations induced by spin-polarized current in a magnetic nanopillar: Analytical versus micromagnetic calculations

We investigate the vortex excitations induced by a spin-polarized current in a magnetic nanopillar by means of micromagnetic simulations and analytical calculations. Damped motion, stationary vortex rotation and the switching of the vortex core are successively observed for increasing values of the current. We demonstrate that even for small amplitude of the vortex motion, the analytical description based the classical Thiele approach can yield quantitatively and qualitatively unsound results. We suggest and validate a new analytical technique based on the calculation of the energy dissipation.

Deflection of a vortex pair by an interface in easy-plane ferromagnets

We study the motion of a vortex–antivortex pair in easy-plane ferromagnets crossing an interface between two media with different anisotropy. A simple description based on the Thiele approach is obtained. The collective variables are the vortex centres and core radii, the latter are assumed to be slaved to the former. For a normal crossing of the interface by the vortex pair, a simple estimate of the ratio of the separation distances is obtained from energy conservation. This prediction is validated by direct numerical simulations of the Landau–Lifshitz equations for the anisotropic Heisenberg model, on a spin lattice divided into two regions which have different anisotropies.

Character analysis in morphological phylogenetics: problems and solutions.

Many aspects of morphological phylogenetics are controversial in the theoretical systematics literature and yet are often poorly explained and justified in empirical studies. In this paper, I argue that most morphological characters describe variation that is fundamentally quantitative, regardless of whether they are coded qualitatively or quantitatively by systematists. Given this view, three fundamental problems in morphological character analysis (definition, delimitation, and ordering of character states) may have a common solution: coding morphological characters as continuous quantitative traits. A new parsimony method (step-matrix gap-weighting, a modification of Thiele's approach) is proposed that allows quantitative traits to be analyzed as continuous variables. The problem of scaling or weighting quantitative characters relative to qualitative characters (and to each other) is reviewed, and three possible solutions are described. The new coding method is applied to data from hoplocercid lizards, and the results show the sensitivity of phylogenetic conclusions to different scaling methods. Although some authors reject the use of continuous, overlapping, quantitative characters in phylogenetic analysis, quantitative data from hoplocercid lizards that are coded using the new approach contain significant phylogenetic structure and exhibit levels of homoplasy similar to those seen in data that are coded qualitatively.