Topological Domains Research Articles

Manipulation of BiFeO3 nanostructure by substrate terrace morphology

Topological domain structures, such as vortex and center domain have been found in BiFeO3 nanoislands fabricated by self-assemble approaches, which exhibit great application potential in nonvolatile storage. However, how to control the self-assembled nanostructure during preparation process is still an open question. Here, we successfully grew BiFeO3 films with nano-stripe, nano-maze and dense nanoisland structures on LaAlO3 (001) substrate by pulsed laser deposition. We found the formation of different nanostructures is related to the terrace morphology of the substrate. Nano-stripe structure with strip domain and high conduction tail-to-tail domain wall preferred to form on wide terrace, nano-maze structure with three-fold or four-fold center-type domain usually form on bunched terrace, while dense nanoisland structure with two/three-fold domain preferred to from on the narrow or rough terrace LaAlO3 substrate. These findings provide guidance for manipulating the ferroelectric topological domain structure during film preparation process.

Origins and Functional Significance of Eukaryotic Protein Folds.

Folds are the architecture and topology of a protein domain. Categories of folds are very few compared to the astronomical number of sequences. Eukaryotes have more protein folds than Archaea and Bacteria. These folds are of two types: shared with Archaea and/or Bacteria on one hand and specific to eukaryotic clades on the other hand. The first kind of folds is inherited from the first endosymbiosis and confirms the mixed origin of eukaryotes. In a dataset of 1073 folds whose presence or absence has been evidenced among 210 species equally distributed in the three super-kingdoms, we have identified 28 eukaryotic folds unambiguously inherited from Bacteria and 40 eukaryotic folds unambiguously inherited from Archaea. Compared to previous studies, the repartition of informational function is higher than expected for folds originated from Bacteria and as high as expected for folds inherited from Archaea. The second type of folds is specifically eukaryotic and associated with an increase of new folds within eukaryotes distributed in particular clades. Reconstructed ancestral states coupled with dating of each node on the tree of life provided fold appearance rates. The rate is on average twice higher within Eukaryota than within Bacteria or Archaea. The highest rates are found in the origins of eukaryotes, holozoans, metazoans, metazoans stricto sensu, and vertebrates: the roots of these clades correspond to bursts of fold evolution. We could correlate the functions of some of the fold synapomorphies within eukaryotes with significant evolutionary events. Among them, we find evidence for the rise of multicellularity, adaptive immune system, or virus folds which could be linked to an ecological shift made by tetrapods.

A hybrid Lagrangian–Eulerian particle finite element method for free‐surface and fluid–structure interaction problems

AbstractThe dynamics of fluid flows with free surfaces and interacting with highly deformable structures is a complex problem, attracting considerable attention. The Particle Finite Element Method (PFEM) is one of the various numerical methods recently proposed in the literature to simulate this type of problems. It is a mesh‐based Lagrangian approach, particularly suited for problems with fast changes in the domain topology, since the fluid boundaries and the Fluid–Structure Interaction (FSI) interface are naturally tracked by the position of the mesh nodes. However, when nonhomogeneous boundary conditions are imposed on velocities or when there are regions where the topology varies moderately, for example, in confined portions of the fluid domain characterized by fixed boundaries, an Eulerian formulation turns out to be more convenient. To exploit the advantages of both formulations, an adaptive hybrid Lagrangian–Eulerian approach is presented in this work. According to the proposed method, nodes on the fluid free‐surface and on the FSI interface are treated as Lagrangian, while the remaining nodes can be either Eulerian or Lagrangian. Furthermore, to increase the efficiency of the method, an algorithm to automatically detect runtime the transition zone between the two kinematic descriptions is devised. To validate the proposed approach, several numerical examples are developed and their results are compared to those available in the literature.

Modeling Object Motion on Arbitrary Unstructured Grids Using an Invariant Principle of Computational Domain Topology: Key Features

This paper uses a finite volume algorithm to address the numerical modeling of fluid flow around moving bodies. The Navier–Stokes equations, which describe the flow of viscous compressible gas, along with key boundary conditions and discretization schemes, are presented. As the motion of boundaries typically leads to changes in the control volumes, the basic discretization schemes need to be adapted. This paper provides a detailed discussion on the adaptation of the initial system to deforming boundaries while preserving communication topology. The method for calculating the boundary velocity is a crucial element of the numerical scheme. The paper proposes an approach to reconstruct the boundary velocity vector using deformation analysis and the condition of geometric conservation. This approach ensures correct simulation results for arbitrary unstructured computational grids. A comparison of two approaches to reconstructing the boundary velocity vector for characteristic aviation problems in the direct formulation is presented. It is shown that the proposed approach allows for more accurate modeling of object motion on arbitrary grids using the “invariant” principle of the computational domain topology.

Observation of dislocation-controlled domain nucleation and domain-wall pinning in single-crystal BaTiO3

Electro-mechanical interactions between topological defects and domain walls play a key role in the macroscopic response of bulk and thin-film ferroelectrics. The applications of ferroelectrics are derived from their inherent ability to nucleate new domains and to move the domain walls that separate adjacent domains. Here, we report dislocation-mediated domain nucleation in single-crystal BaTiO3, achieved by dislocations generated via high-temperature uniaxial compression on a notched sample. We also present a direct observation of domain-wall pinning of 90° ferroelastic domain walls by dislocations using in situ transmission electron microscopy. Dense and well-aligned “forest” dislocations, featuring {100}⟨100⟩ slip systems oriented in the out-of-plane [001] direction, exclusively nucleate in-plane domain variants. We reveal that the 90° domain walls are strongly pinned by imprinted dislocations due to the presence of their associated stress fields. Our findings may advance our understanding of the control of defects in ferroelectrics and propose a strategy applicable to both emerging nanoelectronic and bulk applications.

Lineage-specific 3D genome organization is assembled at multiple scales by IKAROS

A generic level of chromatin organization generated by the interplay between cohesin and CTCF suffices to limit promiscuous interactions between regulatory elements, but a lineage-specific chromatin assembly that supersedes these constraints is required to configure the genome to guide gene expression changes that drive faithful lineage progression. Loss-of-function approaches in B cell precursors show that IKAROS assembles interactions across megabase distances in preparation for lymphoid development. Interactions emanating from IKAROS-bound enhancers override CTCF-imposed boundaries to assemble lineage-specific regulatory units built on a backbone of smaller invariant topological domains. Gain of function in epithelial cells confirms IKAROS' ability to reconfigure chromatin architecture at multiple scales. Although the compaction of the Igκ locus required for genome editing represents a function of IKAROS unique to lymphocytes, the more general function to preconfigure the genome to support lineage-specific gene expression and suppress activation of extra-lineage genes provides a paradigm for lineage restriction.

Physiologic and Transcriptomic Effects Triggered by Overexpression of Wild Type and Mutant DNA Topoisomerase I in Streptococcus pneumoniae.

Topoisomerase I (TopoI) in Streptococcus pneumoniae, encoded by topA, is a suitable target for drug development. Seconeolitsine (SCN) is a new antibiotic that specifically blocks this enzyme. We obtained the topARA mutant, which encodes an enzyme less active than the wild type (topAWT) and more resistant to SCN inhibition. Likely due to the essentiality of TopoI, we were unable to replace the topAWT allele by the mutant topARA version. We compared the in vivo activity of TopoIRA and TopoIWT using regulated overexpression strains, whose genes were either under the control of a moderately (PZn) or a highly active promoter (PMal). Overproduction of TopoIRA impaired growth, increased SCN resistance and, in the presence of the gyrase inhibitor novobiocin (NOV), caused lower relaxation than TopoIWT. Differential transcriptomes were observed when the topAWT and topARA expression levels were increased about 5-fold. However, higher increases (10-15 times), produced a similar transcriptome, affecting about 52% of the genome, and correlating with a high DNA relaxation level with most responsive genes locating in topological domains. These results confirmed that TopoI is indeed the target of SCN in S. pneumoniae and show the important role of TopoI in global transcription, supporting its suitability as an antibiotic target.

A 3D-printed blood-brain barrier model with tunable topology and cell-matrix interactions

Recent developments in digital light processing (DLP) can advance the structural and biochemical complexity of perfusable in vitro models of the blood–brain barrier. Here, we describe a strategy to functionalize complex, DLP-printed vascular models with multiple peptide motifs in a single hydrogel. Different peptides can be clicked into the walls of distinct topologies, or the peptide motifs lining channel walls can differ from those in the bulk of the hydrogel. The flexibility of this approach is used to both characterize the effects of various bioactive domains on endothelial coverage and tight junction formation, in addition to facilitating astrocyte attachment in the hydrogel surrounding the endothelialized vessel to mimic endothelial–astrocyte interaction. Peptides derived from proteins mediating cell-extracellular matrix (e.g. RGD and IKVAV) and cell–cell (e.g. HAVDI) adhesions are used to mediate endothelial cell attachment and coverage. HAVDI and IKVAV-lined channels exhibit significantly greater endothelialization and increased zonula-occluden-1 (ZO-1) localization to cell–cell junctions of endothelial cells, indicative of tight junction formation. RGD is then used in the bulk hydrogel to create an endothelial–astrocyte co-culture model of the blood–brain barrier that overcomes the limitations of previous platforms incapable of complex topology or tunable bioactive domains. This approach yields an adjustable, biofabricated platform to interrogate the effects of cell-matrix interaction on blood–brain barrier mechanobiology.

Modeling, testing, and optimization of novel lattice structures for enhanced mechanical performance

Cellular materials have drawn increasing interest in numerous applications due to their promising specific stiffness, strength and energy absorption capacity. In this work, a variety of rather novel lattice topologies pertinent to additive manufacturing are derived and examined. A number of these are derived by free-domain and constrained domain topology optimization procedures, while others are inspired by the triply periodic minimum surface (TPMS) sheet-based topologies. The topology optimization module utilized a single objective function of minimizing strain energy under linear elastic conditions. A total of fifteen different lattice topologies are investigated numerically, including both novel and conventional topologies (e.g. strut-based lattices) and their effective elastic properties are determined with respect to relative density through finite element analysis (FEA). Based on the preliminary FEA results, a number of these topologies are selected of which tessellated lattice structures are fabricated through laser powder bed fusion (LPBF) additive manufacturing technique out of Nylon thermoplastic material. The tessellated lattice structures are experimentally tested in compression and their mechanical performance, including uniaxial modulus, yield strength, and energy absorption capacity (EAC), is assessed. FEA simulations have been conducted using an elastic-plastic constitutive model for the Nylon base material. Both the experimental and numerical results reveal that the mechanical performance of the novel tube-based TPMS lattice P-100 and the combined loading (CL) topology derived through free-domain topology optimization surpasses all other topologies. P-100 uses a primitive TPMS with equal-length tubular connections in each direction, where the tubular length percentage compared to the primitive lattice size is 100%, while CL lattice topology is a free domain topology optimized under compressive loads on the centers of faces, edges, and vertices toward the center. The innovative lattice topologies proposed in the current study, particularly the P-100 and CL topologies, can become crucial in applications where it is necessary to improve the energy absorption capacity, such as sandwich panel cores, supports, and infills for 3D printed components.

An Algorithm for the Development of a Recombinant Antiherpetic Subunit Vaccine Combining the Crystal Structure Analysis, AlphaFold2-Based Modeling, and Immunoinformatics

Using the envelope glycoprotein B (gB) crystal structure and digital prediction algorithm, the B- and T-cell antigenic determinants (epitopes) of human herpesvirus 1 (HHV-1), also known as herpes simplex virus 1 (HSV-1), were generated, and the method for their production in the form of recombinant proteins was proposed. First, the structure of the surface topological domain (ectodomain or spike) of gB with mapped epitopes was analyzed, and the most stable and immunogenic (due to their enrichment with B-and T-cell epitopes) subdomains were selected for the modeling of subunit vaccine prototypes using the AlphaFold2 (Google DeepMind, London, UK) artificial intelligence system. The proposed candidate vaccines included both small (about 100 amino acids) monomeric polypeptides, which were ideal for recombinant expression as fusion proteins, and a more complex polypeptide, which, due to its trimeric fold, looks like a miniature analog of the gB ectodomain. In this miniature analog, the ectodomain regions with the potential to interfere efficacious expression of soluble recombinant protein in Escherichia coli have been removed. The structural stability of the modeled proteins, confirmed by molecular dynamics simulation and host immune responses, predicted in silico, indicates the suitability of the two suggested polypeptides for generating subunit vaccines using recombinant DNA technology.

A finite element framework for fluid–membrane interactions involving fracture

We propose a novel framework for investigating fluid–membrane interactions involving fracture, and apply it to simulate initial stages during the bursting of a balloon. Fluid flow is computed using a stabilized space–time finite element method over a body-fitted mesh. The membrane is modelled as a hyperelastic material and the equations are solved using the standard Galerkin method. Structural failure is incorporated using the element deletion technique based on a simple strain based criterion. Change in topology of the fluid domain due to element deletion is handled without resorting to remeshing. The coincident fluid nodes on either side of the deleted membrane elements on the surface of the balloon are connected, thereby allowing the fluid to gush through the opening. First, fluid–membrane interaction, without failure, in a square sail with fixed edges is studied. The sail exhibits vibration owing to vortices shed from its edges. We then study the inflation and deflation of a spherical balloon equipped with an inlet pipe. A hydrostatic pressure gradient is applied to drive the flow into the balloon. Effect of different values of membrane density, stiffness and the hydrostatic pressure gradient on inflation rate and balloon shape is studied. The bursting of the inflated balloon is initiated by deleting one structural element on its surface. The proposed algorithm is then applied to simulate the subsequent dynamics of the fluid–membrane system.

Aerodynamic Control of an Inlet Flow in Crosswind Using Peripheral Bleed Actuation

The flow within the inlet of an engine nacelle model in the absence of a fan and the presence of crosswind is investigated in wind-tunnel experiments, with specific emphasis on the effects of separation over the inlet’s inner windward surface on the flow distortion and pressure recovery. The inlet’s entrance plane is tilted forward, and its cross section is asymmetric about the horizontal centerline. The flow topology within the inlet is characterized over a range of Mach numbers and crosswind speeds up to M=0.72 and Uo=18 m/s, respectively. It is shown that in the presence of sufficiently high crosswind to the inlet speed ratio, a three-dimensional horseshoe-like separation domain is formed over the inlet’s inner windward surface. Owing to the cross-sectional asymmetry of the entrance plane, the separation domain migrates azimuthally downward and expands azimuthally with increased crosswind to the inlet speed ratio. The present investigations demonstrate the utility of flow control for mitigating the adverse effects of the separation. The actuation is based on controllable distributed aerodynamic air bleed that is driven by the pressure differences across the nacelle’s inner and outer surfaces and reattaches the separated base flow up to crosswind speeds of 15.4 m/s, resulting in a gain of up to 38% in total pressure recovery and a decrease of up to 55% in total pressure distortion. The efficacy of the bleed actuation can be further improved by tailoring the bleed distribution to the topology of the separated flow domain.

SHIELD: a platform for high-throughput screening of barrier-type DNA elements in human cells

Chromatin boundary elements contribute to the partitioning of mammalian genomes into topological domains to regulate gene expression. Certain boundary elements are adopted as DNA insulators for safe and stable transgene expression in mammalian cells. These elements, however, are ill-defined and less characterized in the non-coding genome, partially due to the lack of a platform to readily evaluate boundary-associated activities of putative DNA sequences. Here we report SHIELD (Site-specific Heterochromatin Insertion of Elements at Lamina-associated Domains), a platform tailored for the high-throughput screening of barrier-type DNA elements in human cells. SHIELD takes advantage of the high specificity of serine integrase at heterochromatin, and exploits the natural heterochromatin spreading inside lamina-associated domains (LADs) for the discovery of potent barrier elements. We adopt SHIELD to evaluate the barrier activity of 1000 DNA elements in a high-throughput manner and identify 8 candidates with barrier activities comparable to the core region of cHS4 element in human HCT116 cells. We anticipate SHIELD could facilitate the discovery of novel barrier DNA elements from the non-coding genome in human cells.

A topology-based in-plane filtering technique for the combined topology and discrete fiber orientation optimization

This work proposes a filtering technique for the concurrent and sequential finite element-based topology and discrete fiber orientation optimization of composite structures. The proposed filter is designed to couple the morphology with the topology of the structural domain throughout the optimization process in a way such that it suppresses the impact of the close-to-void finite elements’ morphology on the overall morphology of the structure while steering at the same time the local fiber orientation towards the neighboring topologically dense areas of the geometry. The functionality of the filter becomes crucial at the boundaries of the optimized structure, where the fiber orientation is forced to conform to the morphology of the local boundaries. The developed filtering technique is incorporated into both the concurrent and sequential finite element-based topology and discrete fiber orientation optimization problem, and the respective optimization problems are formulated for the compliance minimization of the composite structure. To assess the efficacy of the filter, it is demonstrated in the benchmark academic case studies of the 2D Messerschmitt-Bölkow-Blohm and cantilever beams when different state-of-art interpolation techniques are employed for modeling the discrete fiber orientation optimization problem.

Composing topological domain walls and anyon mobility

Topological domain walls separating 2+1 dimensional topologically ordered phases can be understood in terms of Witt equivalences between the UMTCs describing anyons in the bulk topological orders. However, this picture does not provide a framework for decomposing stacks of multiple domain walls into superselection sectors — i.e., into fundamental domain wall types that cannot be mixed by any local operators. Such a decomposition can be understood using an alternate framework in the case that the topological order is anomaly-free, in the sense that it can be realized by a commuting projector lattice model. By placing these Witt equivalences in the context of a 3-category of potentially anomalous (2+1)D topological orders, we develop a framework for computing the decomposition of parallel topological domain walls into indecomposable superselection sectors, extending the previous understanding to topological orders with non-trivial anomaly. We characterize the superselection sectors in terms of domain wall particle mobility, which we formalize in terms of tunnelling operators. The mathematical model for the 3-category of topological orders is the 3-category of fusion categories enriched over a fixed unitary modular tensor category.

Composite topological solitons consisting of domain walls, strings, and monopoles in O(N) models

We study various composites of global solitons consisting of domain walls, strings, and monopoles in linear O(N) models with N = 2 and 3. Spontaneous symmetry breaking (SSB) of the O(N) symmetry down to O(N – 1) results in the vacuum manifold SN−1, together with a perturbed scalar potential in the presence of a small explicit symmetry breaking (ESB) interaction. The O(2) model is equivalent to the axion model admitting topological global (axion) strings attached by NDW domain walls. We point out for the NDW = 2 case that the topological stability of the string with two domain walls is ensured by sequential SSBs (ℤ2)2 → ℤ2 → 1, where the first SSB occurs in the vacuum leading to the topological domain wall as a mother soliton, only inside which the second SSB occurs giving rise to a subsequent kink inside the mother wall. From the bulk viewpoint, this kink is identical to a global string as a daughter soliton. This observation can be naturally ex- tended to the O(3) model, where a global monopole as a daughter soliton appears as a kink in a mother string or as a vortex on a mother domain wall, depending on ESB interactions. In the most generic case, the stability of the composite system consisting of the monopole, string, and domain wall is understood by the SSB (ℤ2)3 → (ℤ2)2 → ℤ2 → 1, in which the first SSB at the vacuum gives rise to the domain wall triggering the second one, so that the daughter string appears as a domain wall inside the mother wall triggering the third SSB, which leads to a granddaughter monopole as a kink inside the daughter vortex. We demonstrate numerical simulations for the dynamical evolution of the composite solitons.

Features of Protein Unfolding Transitions and Their Relation to Domain Topology Probed by Single-Molecule FRET.

A protein fold is defined as a structural arrangement of a secondary structure in a three-dimensional space. It would be interesting to know whether a particular fold can be assigned to certain features of the corresponding folding/unfolding transitions. To understand the underlying principles of the manifold folding transitions in more detail, single-molecule FRET is the method of choice. Taking the two-domain protein phosphoglycerate kinase (PGK) as an example, we investigated denaturant-induced unfolded states of PGK using the above method. For this purpose, different intramolecular distances within the two domains were measured. In addition to the known two-state transition, a transition with a compact folding intermediate was also identified in each of the two domains. Based on the structural homology of the domains (characterized by a Rossmann fold) and the striking similarity in the features of the measured distance changes during unfolding, clear evidence emerged that the underlying domain topology plays an important role in determining the observed structural changes.

Model order reduction for deforming domain problems in a time‐continuous space‐time setting

AbstractIn the context of simulation‐based methods, multiple challenges arise, two of which are considered in this work. As a first challenge, problems including time‐dependent phenomena with complex domain deformations, potentially even with changes in the domain topology, need to be tackled appropriately. The second challenge arises when computational resources and the time for evaluating the model become critical in so‐called many query scenarios for parametric problems. For example, these problems occur in optimization, uncertainty quantification (UQ), or automatic control, and using highly resolved full‐order models (FOMs) may become impractical. To address both types of complexity, we present a novel projection‐based model order reduction (MOR) approach for deforming domain problems that takes advantage of the time‐continuous space‐time formulation. We apply it to two examples that are relevant to engineering or biomedical applications and conduct an error and performance analysis. In both cases, we are able to drastically reduce the computational expense for a model evaluation and, at the same time, maintain an adequate accuracy level, each compared to the original time‐continuous space‐time full‐order model (FOM). All in all, this work indicates the effectiveness of the presented MOR approach for deforming domain problems by taking advantage of a time‐continuous space‐time setting.

Quantitative morphometry of topological graphene-based aerogels and carbon foams by x-ray micro-computed tomography

In this work, we report quantitative morphometry of freeze-dried graphene-based aerogels (i.e., graphene aerogel-GA, nitrogenated GA-NGA, graphene-carbon nanotube hybrid-Gr-MWCNTs, carbon foam-CF, and CF-GA hybrid-CF-GA) and monoliths, prepared by hydrothermal and organic sol-gel methods, respectively. X-ray micro-computed tomography (XMCT) in combination with scanning and transmission electron microscopy allowed visualization of internal microstructures in three-dimensional space. Quantitative morphometry analysis through the reconstructed volume renderings from two-dimensional sliced images revealed hierarchical structures possessing interlaced thin sheets, honeycomb organization, and topological interconnected pore background domains. The influence of small-diameter functionalized multi-walled carbon nanotubes (MWCNTs) inclusions to graphene-like sheets and integration with CF is assessed through quantitative morphometry analysis in terms of volume-weighted pore size, wall thickness, and porosity levels. Hybrid composite porous solids elucidated cross-linking reinforced by a homogeneous distribution of CNTs into complex sheets of GA and CF matrices. A consistent trend impacting porosity and interconnectedness was found following NGA ≥ GA > CF > Gr-MWCNT2:1 > CF-GA > Gr-MWCNT3:1 > Gr-MWCNT5:1, from XMCT image processing and analyses in corroboration with physical properties and reliability. The experimental results provide insights and guide the design of characteristic porous carbonaceous and graphene-based functional nanomaterials for energy sciences, environmental engineering, and fundamental reactive transport of fluids.

The Effect of the Domain Topology on the Number of Positive Solutions for Fractional p-laplacian Equation with Critical Growth

The Effect of the Domain Topology on the Number of Positive Solutions for Fractional p-laplacian Equation with Critical Growth