Topological Textures Research Articles

Effect of lithium salt concentrations on blended 49% poly(methyl methacrylate) grafted natural rubber and poly(methyl methacrylate) based solid polymer electrolyte

The effect of lithium salts (lithium tetrafluoroborate, LiBF 4 and lithium perchlorate, LiClO 4) as doping salts in rubber-polymer blends, 49% poly(methyl methacrylate) grafted natural rubber (MG49) and poly(methyl methacrylate) (PMMA) in solid polymer electrolyte (SPE) film for electrochemical devices application was investigated. The electrolyte films were prepared via the solution casting technique using 0–25 wt.% lithium salt. The effect of the lithium salts on chemical interaction, ionic conductivity and structural and morphological studies of (70:30) MG49-PMMA films was analyzed using Fourier Transform Infrared (FT-IR) Spectroscopy, Electrochemical Impedance Spectroscopy (EIS), X-ray Diffraction (XRD) and Scanning Electron Microscopy (SEM). Infrared analysis showed that the interactions between lithium ions and oxygen atoms occur at the ether group (C–O–C) (1500–1100 cm −1) on the MMA structure in both MG49 and PMMA. The oxygen atoms in the structure of the polymer host act as electron donor atoms and form a coordinate bond with the lithium ions from the doping salt to form polymer–salt complexes. The ionic conductivity was investigated at room temperature as well as at a temperature range from 303 K to 373 K. The ionic conductivity without the addition of salt was 1.1 × 10 −12 S cm −1. The highest conductivity at room temperature for (70:30) MG49-PMMA–LiBF 4 was 8.6 × 10 −6 S cm −1 at 25 wt.% of LiBF 4. The ionic conductivity of (70:30) MG49-PMMA–LiClO 4 was 1.5 × 10 −8 S cm −1 at 25 wt.% of LiClO 4. However, both electrolyte systems do not exhibit Arrhenius-like behavior. Systems with LiBF 4 salt have higher ionic conductivity than those with LiClO 4 salt because of the differences in anionic size and lattice energy of the appropriate salt. The observations from structural and morphology studies showed that complexation and re-crystallization occur in the system. The XRD studies showed a reduction of the MMA peak intensity at 29.5° after the addition of 5–25 wt.% LiBF 4 salt due to ion dissociation in the electrolyte system. Thus, this contributed to the increase of ionic conductivity in (70:30) MG49-PMMA–LiBF 4. Morphological studies showed that (70:30) MG49-PMMA is homogenously blended, and no phase separation occurred. The addition of lithium salts changed the topological texture from a smooth and dark surface to a rough and bright surface.

Topological Phase Transition and Texture Inversion in a Tunable Topological Insulator

The recently discovered three-dimensional or bulk topological insulators are expected to exhibit exotic quantum phenomena. It is believed that a trivial insulator can be twisted into a topological state by modulating the spin-orbit interaction or the crystal lattice, driving the system through a topological quantum phase transition. By directly measuring the topological quantum numbers and invariants, we report the observation of a phase transition in a tunable spin-orbit system, BiTl(S(1-δ)Se(δ))(2), in which the topological state formation is visualized. In the topological state, vortex-like polarization states are observed to exhibit three-dimensional vectorial textures, which collectively feature a chirality transition as the spin momentum-locked electrons on the surface go through the zero carrier density point. Such phase transition and texture inversion can be the physical basis for observing fractional charge (±e/2) and other fractional topological phenomena.

Performance of topological texture features to classify fibrotic interstitial lung disease patterns

Topological texture features were compared in their ability to classify "honeycombing," a morphological pattern that is considered indicative for the presence of fibrotic interstitial lung disease in high-resolution computed tomography (HRCT) images. For 14 patients with known occurrence of honeycombing, a stack of 70 axial, lung kernel reconstructed images was acquired from HRCT chest exams. A set of 964 regions of interest of both healthy and pathological (356) lung tissue was identified by an experienced radiologist. Texture features were extracted using statistical features (Stat), six properties calculated from gray-level co-occurrence matrices (GLCMs), Minkowski dimensions (MDs), and three Minkowski functionals (MFs) (e.g., MF.Euler). A naïve Bayes (NB) and k-nearest-neighbor (k-NN) classifier, a multilayer radial basis functions network (RBFN), and a support vector machine with a radial basis function (SVMrbf) kernel were optimized in a tenfold cross-validation for each texture vector, and the classification accuracy was calculated on independent test sets as a quantitative measure of automated tissue characterization. A Wilcoxon signed-rank test was used to compare two accuracy distributions and the significance thresholds were adjusted for multiple comparisons by the Bonferroni correction. The best classification results were obtained by the MF features, which performed significantly better than all the standard Stat, GLCM, and MD features (p < 0.001) for both classifiers. The highest accuracies were found for MF.Euler (93.6%, 94.9%, 94.2%, and 95.0% for NB, k-NN, RBFN, and SVMrbf, respectively). The best groups of standard texture features were a Stat and GLCM ("homogeneity") feature set (up to 91.8%). The results indicate that advanced topological texture features derived from MFs can provide superior classification performance in computer-assisted diagnosis of fibrotic interstitial lung disease patterns when compared to standard texture analysis methods.

Automatic differentiation of micromechanics incremental schemes for coupled fields composite materials: Effective properties and their sensitivities

A modeling approach based on automatic differentiation and micromechanics incremental schemes for coupled fields composite materials is presented in this work. In the multi-sites framework, the micromechanics incremental schemes presented herein are able to account for the anisotropic behavior of the constituents, the morphological and the topological textures and the strong contrast between the properties of the individual phases of these composite materials. By applying automatic differentiation to these micromechanics incremental schemes, the first order and high order sensitivities of the effective material properties can be easily computed in the same analysis. An application on three-phase magneto-electro-elastic composite material is presented in the framework of mono-site micromechanics to show the effectiveness of this composite materials modeling approach. The details on the implementation of this modeling approach in the multi-sites framework will be discussed in a future work. The composite materials modeling methodology reported here may be used for material microstructure sensitive design in material by design strategies.

Stable topological textures in a classical two-dimensional Heisenberg model

We show that stable localized topological soliton textures (skyrmions) with ${\ensuremath{\pi}}_{2}$ topological charge $\ensuremath{\nu}\ensuremath{\ge}1$ exist in a classical two-dimensional Heisenberg model of a ferromagnet with uniaxial anisotropy. For this model the soliton exists only if the number of bound magnons exceeds some threshold value ${N}_{\text{cr}}$ depending on $\ensuremath{\nu}$ and the effective anisotropy constant ${K}_{\text{eff}}$. We define soliton phase diagram as the dependence of threshold energies and bound magnons number on anisotropy constant. The phase boundary lines are monotonous for both $\ensuremath{\nu}=1$ and $\ensuremath{\nu}&gt;2$ while the solitons with $\ensuremath{\nu}=2$ reveal peculiar nonmonotonous behavior, determining the transition regime from low to high topological charges. In particular, the soliton energy per topological charge (topological energy density) achieves a minimum neither for $\ensuremath{\nu}=1$ nor high charges but rather for intermediate values $\ensuremath{\nu}=2$ or $\ensuremath{\nu}=3$. We show that this peculiarity is related to the character of convergence of integrals defining soliton energy and number of bound magnons at different $\ensuremath{\nu}$.

Automated classification of normal and pathologic pulmonary tissue by topological texture features extracted from multi-detector CT in 3D

To provide a novel, robust algorithm for classification of lung tissue depicted by multi-detector computed tomography (MDCT) based on the topology of CT-attenuation values and to compare discriminative results with densitometric methods. Two hundred seventy-five cubic volumes of interest (VOI, edge length 40 pixels) were obtained from MDCT chest CT (isotropic voxel size, edge length 0.6 mm) of 21 subjects with and without pathology (emphysema, fibrosis). All VOIs were visually consensus-classified by two radiologists. Texture features based on the Minkowski functionals (MF) as well as on the CT attenuation values are determined. Classification results of both approaches were assessed by receiver-operator characteristic and discriminant analysis. By densitometric (topological) parameters, normal and abnormal VOIs were distinguished with an area under the curve ranging from 0.78 to 0.85 (0.87 to 0.96). Correlation between both groups of parameters was non-significant (p > or = 0.36). By combined information of densitometric and topological quantities, the radiologists' ratings were reproduced for 92% of VOIs, ranging from 85.7% (fibrosis) to 98% (normal VOIs). Our method performs well for identification of VOIs containing abnormal lung-tissue. Combined information of densitometry and topology increases the number of correctly classified VOIs further. When extended to CT data depicting whole lungs, topological analysis may allow to enhance density-based analysis and improve monitoring texture changes with progression of pulmonary disease.

Theory of helical spin crystals: Phases, textures, and properties

Motivated by recent experiments on the itinerant helimagnet MnSi, we study general properties of helical spin crystals - magnetic structures obtained by superposing distinct spin spirals. An effective Landau description of helical spin crystals is introduced and simple rules for stabilizing various spin crystal structures over single spirals are established. Curious properties of the magnetic structures so obtained, such as symmetry stabilized topological textures and missing Bragg reflections are pointed out. The response of helical spin crystals to crystalline anisotropy, magnetic field and non-magnetic disorder are studied, with special reference to the bcc1 spin structure, a promising starting point for discussing the 'partial order' phases seen at high pressure in MnSi. Similar approaches may be applied to other crystallization problems such as Larkin-Ovchinnikov-Fulde-Ferrel states in spin-imbalanced superconductors.

Discovery of a honeycomb structure in the twisted plywood patterns of fibrous biological nanocomposite tissue

Electron microscopy and synchrotron Bragg diffraction were used for the investigation of the structure of the exoskeleton of the lobster Homarus americanus. The study reveals a pronounced microstructure hierarchy and a strong crystallographic and topological texture of the α-chitin–protein network underlying the twisted plywood (Bouligand) structure. The results suggest that the classical picture of such structures must be refined. Instead of a smoothly misoriented stacking sequence of its constitutive nanofibrous chitin–protein planes, two major and two minor orientation branches of the fibers perpendicular to a common 〈020〉 crystallographic axis pointing towards the surface of the cuticle were found. This crystallographic texture confirms the microscopical observation that the chitin–protein arrays which form the structural subunits of plywood patterns assume the form of planar honeycombs.

Topological stripelike coreless textures with inner incommensurability in two-dimensional Heisenberg antiferromagnet

For two-dimensional Heisenberg antiferromagnet we present an analysis of topological coreless excitations having a stripe form. These textures are characterized by singularities at boundaries. A detailed classification of the stripe textures results in a certain analogy with the coreless excitations in $^3He-A$ phase: Mermin-Ho and Anderson-Toulouse coreless vortices. The excitations of the last type may have a low bulk energy. The stripe textures may be observed as an occurrence of short-range incommensurate order in the antiferromagnetic environment.

Magnet/Superconductor Nanostructures

In Magnet/Superconductor Nanostructures it is possible to control magnetism and conductivity at the nanoscale by using localized magnetic fields from structural (dots, stripes, wires) and topological (vortices's, skyrmions and domain walls) textures in magnet and/or superconductor subsystems of the hybrid material. We review experimental and theoretical results in the field of nanostructured magnet/superconductor systems.

Fractional quantum Hall effect, Jain’s rule, and topological textures

It is demonstrated that Jain’s rule for determining fractions in the quantum Hall effect can be obtained without recourse to the phenomenological concept of composite fermions. The possibility of existence is considered for topologically nontrivial many-electron wave functions, whose group classification gives an indication of special values of electron density in the ground states separated by a gap from excited energies.

Dynamics of orientational ordering in fluid membranes.

We study the dynamics of orientational phase ordering in fluid membranes. Through numerical simulation we find an unusually slow coarsening of topological texture, which is limited by subdiffusive propagation of membrane curvature. The growth of the orientational correlation length xi obeys a power law xi proportional, variant t(w) with w<1/4 in the late stage. We will also discuss defect profiles and correlation patterns in terms of long-range interaction mediated by curvature elasticity.

Chiral phase transition in dissipative dynamics

Numerical simulations of the chiral phase transition in the (3+1)-dimensional $O(4)$ model are presented. The evolutions of the chiral field follow purely dissipative dynamics, starting from random chirally symmetric initial configurations down to the true vacuum with spontaneously broken symmetry. The model stabilizes topological textures which are formed together with domains of a disoriented chiral condensate (DCC) during the roll-down phase. The classically evolving field acts as a source for the emission of pions and $\ensuremath{\sigma}$ mesons. The exponents of power laws for the growth of angular correlations and for emission rates are extracted. Fluctuations in the abundance ratios for neutral and charged pions are compared with those for uncorrelated sources as a potential signature for the chiral phase transition after heavy-ion collisions. It is found that the presence of stabilizing textures (baryons and antibaryons) prevents the sufficiently rapid growth of the DCC domain size, so observability of anomalous tails in the abundance ratios is unlikely. However, the transient formation of growing DCC domains causes sizable broadening of the distributions as compared to the statistical widths of generic sources.

Disoriented chiral condensate dynamics in the(2+1)DO(3)model

The dynamics of symmetry breaking after a quench is numerically simulated on a lattice for the (2+1)-dimensional $O(3)$ model. In addition to the standard sigma model with a temperature-dependent ${\ensuremath{\Phi}}^{4}$ potential the energy functional includes a four-derivative current-current coupling to stabilize the size of the emerging extended topological textures. The total winding number can be conserved by constraint. As a model for the chiral phase transition during the cooling phase after a hadronic collision this allows us to investigate the interference of ``baryon-antibaryon'' production with the developing disoriented aligned domains. The growth of angular correlations, condensate, and average orientation is studied in dependence of texture size, quench rate, and symmetry breaking. The classical dissipative dynamics determines the rate of energy emitted from the relaxing source for each component of the 3-vector field which provides a possible signature for the domains of disoriented chiral condensate (DCC). We find that the ``pions'' are emitted in two distinct pulses; for sufficiently small lattice size the second one carries the DCC signal, but it is strongly suppressed as compared to simultaneous ``sigma''-meson emission. We compare the resulting anomalies in the distributions of DCC pions with probabilities derived within the commonly used coherent state formalism.

Signature of the staggered flux state around a superconducting vortex in underdoped cuprates

Based on the SU(2) lattice-gauge-theory formulation of the $t\ensuremath{-}J$ model, we discuss a possible signature of the unit-cell doubling associated with the staggered-flux (SF) state in the lightly doped spin liquid. Although the SF state appears only dynamically in a uniform d-wave superconducting state, a topological defect [SU(2) vortex] freezes the SF state inside the vortex core. Consequently, the unit-cell doubling shows up in the hopping $({\ensuremath{\chi}}_{\mathrm{ij}})$ and pairing $({\ensuremath{\Delta}}_{\mathrm{ij}})$ order parameters of physical electrons. We find that whereas the center in the vortex core is a SF state, as one moves away from the core center, a correlated staggered modulation of ${\ensuremath{\chi}}_{\mathrm{ij}}$ and ${\ensuremath{\Delta}}_{\mathrm{ij}}$ becomes predominant. We predict that over the region outside the core and inside the internal gauge-field-penetration depth around a vortex center, the local density of states exhibits a staggered peak-dip (SPD) structure inside the V-shaped profile when measured on the bonds. The SPD structure has its direct origin in the unit-cell doubling associated with the SF core and the robust topological texture, which has little to do with the symmetry of the d-wave order parameter. Therefore the structure may survive the tunneling-matrix-element effects and easily be detected by the scanning-tunnel-microscope experiment.

Unraveling critical dynamics: The formation and evolution of textures

We study the formation of topological textures in a nonequilibrium phase transition of an overdamped classical O(3) model in 2+1 dimensions. The phase transition is triggered through an external, time-dependent effective mass, parameterized by quench timescale \tau. When measured near the end of the transition the texture separation and the texture width scale respectively as \tau^(0.39 \pm 0.02) and \tau^(0.46 \pm 0.04), significantly larger than \tau^(0.25) predicted from the Kibble-Zurek mechanism. We show that Kibble-Zurek scaling is recovered at very early times but that by the end of the transition the power-laws result instead from a competition between the length scale determined at freeze-out and the ordering dynamics of a textured system. In the context of phase ordering these results suggest that the multiple length scales characteristic of the late-time ordering of a textured system derive from the critical dynamics of a single nonequilibrium correlation length. In the context of defect formation these results imply that significant evolution of the defect network can occur before the end of the phase transition. Therefore a quantitative understanding of the defect network at the end of the phase transition generally requires an understanding of both critical dynamics and the interactions among topological defects.

Collapse of topological texture

We study analytically the process of a topological texture collapse in the approximation of a scaling ansatz in the nonlinear sigma-model. In this approximation we show that in flat space-time topological texture eventually collapses while in the case of spatially flat expanding universe its fate depends on the rate of expansion. If the universe is inflationary, then there is a possibility that texture will expand eternally; in the case of exponential inflation the texture may also shrink or expand eternally to a finite limiting size, although this behavior is degenerate. In the case of power law noninflationary expansion topological texture eventually collapses. In a cold matter dominated universe we find that texture which is formed comoving with the universe expansion starts collapsing when its spatial size becomes comparable to the Hubble size, which result is in agreement with the previous considerations. In the nonlinear sigma-model approximation we consider also the final stage of the collapsing ellipsoidal topological texture. We show that during collapse of such a texture at least two of its principal dimensions shrink to zero in a similar way, so that their ratio remains finite. The third dimension may remain finite (collapse of cigar type), or it may also shrink to zero similar to the other two dimensions (collapse of scaling type), or shrink to zero similar to the product of the remaining two dimensions (collapse of pancake type).

Generating Spacetimes of Zero Gravitational Mass

We propose a geometric ansatz, a restriction on Euclidean / Minkowski distance in the embedding space being propotional to distance in the embedded space, to generate spacetimes with vanishing gravitational mass ($R_{ik} u^i u^k = 0, u_i u^i = 1 $). It turns out that these spacetimes can represent global monopoles and textures. Thus the ansatz is a prescription to generate zero mass spacetimes that could describe topological defects, global monopoles and textures.

Inhomogeneous states of nonequilibrium superconductors: Quasiparticle bags and antiphase domain walls

Nonequilibrium properties of short-coherence-length $s$-wave superconductors are analyzed in the presence of extrinsic and intrinsic inhomogeneities. In general, the lowest-energy configurations of quasiparticle excitations are topological textures into which quasiparticles segregate and that are described as antiphase domain walls between superconducting regions whose order parameter phases differ by $\ensuremath{\pi}$. Antiphase domain walls can be probed by various experimental techniques, for example, by optical absorption and NMR. At zero temperature, quasiparticles seldom appear as self-trapped bag states. However, for low concentrations of quasiparticles, they may be stabilized in superconductors by extrinsic defects.

Spin textures in quantum Hall droplets

Abstract We have analyzed spin waves and topological textures in a quantum Hall droplet. For spin waves we present a simple scheme to study scattering at the boundary of the system obtaining analytical expressions for the low-energy excitations which turn out to be edge spin textures. From this simple description we perform a study of edge reconstruction of a quantum Hall ferromagnet. Edge spin textures are responsible for the low-temperature dependence of the magnetization. As far as topological textures are concerned, we describe bulk-charged skyrmions as spin waves localized around a topological defect. They can be expressed as a condensate of spin excitons interacting via a two-body repulsive interaction. This framework allows the calculation of the skyrmion energy as a function of its size.