Topological Density Research Articles

Skyrmion ground state and gyration of skyrmions in magnetic nanodisks without the Dzyaloshinsky-Moriya interaction

We show by micromagnetic simulations that a spontaneous skyrmion ground state can exist in Co/Ru/Co nanodisks without the Dzyaloshinsky-Moriya interaction, which can remain stable in the applied magnetic field along the $+$$z$ direction even up to 0.44 T. The guiding center (${R}_{x}$,${R}_{y}$) of skyrmion defined by the moments of the topological density presents a gyration with a star-like trajectory in a pulsed magnetic field and a hexagonal trajectory after the field is switched off, which is different from that of a vortex or bubble. One of the coupled skyrmions could move without an external magnetic field, just induced by the motion of the other one due to strong interlayer magnetostatic interactions. This work sheds light on how skyrmions can be discovered in various (not limited to magnetic) systems with competing energies and contributes to the understanding of the dynamical properties of skyrmions.

Nanofiber density determines endothelial cell behavior on hydrogel matrix

When cultured under static conditions, bacterial cellulose pellicles, by the nature of the polymer synthesis that involves molecular oxygen, are characterized by two distinct surface sides. The upper surface is denser in fibers (entangled) than the lower surface that shows greater surface porosity. Human umbilical vein endothelial cells (HUVECs) were used to exploit how the microarchitecture (i.e., surface porosity, fiber network structure, surface topology, and fiber density) of bacterial cellulose pellicle surfaces influence cell–biomaterial interaction and therefore cell behavior. Adhesion, cell ingrowth, proliferation, viability and cell death mechanisms were evaluated on the two pellicle surface sides. Cell behavior, including secondary necrosis, is influenced only by the microarchitecture of the surface, since the biomaterial is extremely pure (constituted of cellulose and water only). Cell–cellulose fiber interaction is the determinant signal in the cell–biomaterial responses, isolated from other frequently present interferences such as protein and other chemical traces usually present in cell culture matrices. Our results suggest that microarchitecture of hydrogel materials might determine the performance of biomedical products, such as bacterial cellulose tissue engineering constructs (BCTECs).

Gravity asymptotics with topological parameters

In four dimensional gravity theory, the Barbero-Immirzi parameter has a topological origin, and can be identified as the coefficient multiplying the Nieh-Yan topological density in the gravity Lagrangian, as proposed by Date et al.[1]. Based on this fact, a first order action formulation for spacetimes with boundaries is introduced. The bulk Lagrangian, containing the Nieh-Yan density, needs to be supplemented with suitable boundary terms so that it leads to a well-defined variational principle. Within this general framework, we analyse spacetimes with and without a cosmological constant. For locally Anti de Sitter (or de Sitter) asymptotia, the action principle has non-trivial implications. It admits an extremum for all such solutions provided the SO(3,1) Pontryagin and Euler topological densities are added to it with fixed coefficients. The resulting Lagrangian, while containing all three topological densities, has only one independent topological coupling constant, namely, the Barbero-Immirzi parameter. In the final analysis, it emerges as a coefficient of the SO(3,2) (or SO(4,1)) Pontryagin density, and is present in the action only for manifolds for which the corresponding topological index is non-zero.

A computational acumen into the relative applicability of geometrical and quantum chemical criteria in assessing intramolecular hydrogen bonding (IMHB) interaction: 5-Halosalicylic acids as representative examples

Density functional theory (DFT) based computational study has been performed to characterize intramolecular hydrogen bonding (IMHB) interaction in a series of salicylic acid derivatives having different halogen substitution at the 5-position on the benzene ring. The molecular systems studied are salicylic acid (SA), 5-fluorosalicylic acid (5FSA), 5-chlorosalicylic acid (5ClSA) and 5-bromosalicylic acid (5BrSA). Particular emphasis has been given on the analysis of IMHB interaction by the calculation of electron density ρ(r) and Laplacian ∇2ρ(r) at the bond critical point using Atoms-In-Molecule (AIM) theory. Topological features and energy densities based on ρ(r) through the perturbation of the IMHB distances suggest that at equilibrium geometry the IMHB interaction develops certain characteristics typical of a covalent interaction. Concomitantly, the role of charge transfer interaction in the IMHB has been critically addressed under the provision of Natural Bond Orbital (NBO) analysis. The formation of Resonance Assisted Hydrogen Bond (RAHB) in the studied molecular systems is also delineated from quantum chemical calculations. The interplay between aromaticity and RAHB is discussed in this context using both geometrical and magnetic criteria as the aromaticity descriptors. The optimized geometry features, analysis of the molecular electrostatic potential map have also been found to produce a consensus view in relation with the formation of RAHB in the studied systems. The lack of a specific pattern of IMHB energy in the studied molecules with the electronegativity of the substituent has also been attempted to address critically. Another major aspect of the present study is the argument about the superiority of quantum chemical criteria over geometrical criteria for the assessment of IMHB interaction in the studied compounds.

Torque Density of Radial, Axial and Transverse Flux Permanent Magnet Machine Topologies

Torque density of radial, axial and transverse flux machine topologies is investigated. A 10-kW, 200-rpm motor is chosen as a test case. Radial and axial flux motors that fulfill the key specifications of the selected test case are designed employing in-house analytical dimensioning tools and MATLAB genetic multi-objective optimization. Rather simple numerical approach is taken to study the transverse flux motor. A 20-pole-pair radial flux motor is found to outperform its axial and transverse flux counterparts in terms of torque density.

Hydrogen-bonded complexes of serotonin with methanol and ethanol: a DFT study

Density functional theoretical studies on hydrogen-bonded complexes of serotonin with methanol/ethanol have been carried out in a systematic way. The conformational analysis led to ten stable conformers that can be either gauche or anti depending on the dihedral angle values taken by ethylamine side chain and the 5-hydroxyl group. Serotonin-molecules strongly bind with ethanol than methanol. Ethylamine side chain is the most reactive site in both methanol/ethanol complexes and it is responsible for the stability order. The topological parameters, electron density, and Laplacian of electron density show excellent correlation with the hydrogen bond length. Natural bond orbital analysis confirms C–H···O hydrogen bond formed between the serotonin–alcohol complexes to be red shift in nature except for Gph(out)anti complex both with methanol and ethanol to be blue shifted. The energy decomposition analysis reveals that strong interactions between serotonin and ethanol/methanol are due to the attractive contributions from the electrostatic component.

Electronic properties and fermi surface for new Fe-free layered pnictide-oxide superconductor BaTi2Bi2O from first principles

Very recently, as an important step in the development of layered Fe-free pnictide-oxide superconductors, the new phase BaTi2Bi2O was discovered which has the highest TC (about 4.6 K) among all related non-doped systems. In this Letter, we report for the first time the electronic bands, Fermi surface topology, total and partial densities of electronic states for BaTi2Bi2O obtained by means of the first-principles FLAPW-GGA calculations. The inter-atomic bonding picture is described as a high-anisotropic mixture of metallic, covalent, and ionic contributions. Besides, the structural and electronic factors, which can be responsible for the increased transition temperature for BaTi2Bi2O (as compared with related pnictide-oxides BaTi2As2O and BaTi2Sb2O), are discussed.

Structural, electronic properties, and chemical bonding in quaternary layered titanium pnictide-oxides Na2Ti2Pn2O and BaTi2Pn2O (Pn = As, Sb) from FLAPW–GGA calculations

By means of the first-principles FLAPW–GGA calculations, we have investigated the main trends in structural, electronic properties, and chemical bonding for a series of quaternary titanium pnictide-oxides: Na2Ti2As2O, Na2Ti2Sb2O, BaTi2As2O, and BaTi2Sb2O, which attracted now much attention as parent phases for a novel group of layered Fe-free superconducting materials. Our results cover the optimized lattice parameters and atomic positions, electronic bands, Fermi surface topology, total and partial density of electronic states. Besides, Bader analysis and the charge density maps are used to discuss the chemical bonding for the examined materials. We find that the atomic substitutions lead to anisotropic deformation of the crystal structure; this effect is related to strong anisotropy of inter-atomic bonds, which are of a mixed (covalent-ionic-metallic) type – in blocks [Ti2Pn2O], whereas the bonding between blocks [Ti2Pn2O] and atomic sheets of Na, Ba ions is of an ionic type. The actual effective atomic charges differ from the formal ionic charges due to covalency in blocks [Ti2Pn2O]. The near-Fermi electronic bands, which are responsible for metallic-like behavior of these materials and will be involved in the formation of superconducting state, arise mainly from the Ti 3dxy, dx2−y2, and dz2 states of the blocks [Ti2Pn2O], which define also the anisotropic character of conduction happening mainly in these blocks. The differences in the topology of the multi-sheet Fermi surfaces of these materials are discussed.

Topological defects and density fluctuations in collectively moving systems

Ensembles of collectively moving particles like flocks of birds, bacteria, or filamentous polymers show a broad range of intriguing phenomena, yet seem to obey very similar physical principles. These generic principles have been predicted to lead to characteristic density fluctuations, which are in sharp contrast to normal fluctuations determining the properties of ordered systems in thermal equilibrium. Using high-density motility assays of driven filaments, we characterize here the origin and nature of giant fluctuations that emerge in this class of systems. By showing that these unique statistical properties result from the coupling between particle density and the topology of the velocity field of the particles, we provide insight in the physics of collective motion.

Transport and drift-driven plasma flow components in the Alcator C-Mod boundary plasma

Boundary layer flows in the Alcator C-Mod tokamak are systematically examined as magnetic topology (upper versus lower-null) and plasma density are changed. Utilizing a unique set of scanning Langmuir–Mach probes, including one on the high-field side (HFS) midplane, the poloidal variation of plasma flow components in the parallel, diamagnetic and radial directions are resolved in detail. It is found that the plasma flow pattern can be decomposed into two principal parts: (1) a drift-driven component, which lies within a magnetic flux surface and is divergence-free and (2) a transport-driven component, which gives rise to near-sonic parallel flows on the HFS scrape-off layer (SOL). Toroidal rotation, Pfirsch–Schlüter and transport-driven contributions are unambiguously identified. Transport-driven parallel flows are found to dominate the HFS particle fluxes; the total poloidal-directed flow accounts for ∼1/3 to all of the ion flux arriving on the inner divertor. As a result, heat convection is found to be an important player in this region, consistent with the observation of divertor asymmetries that depend on the direction of B × ∇B relative to the active x-point. In contrast, the poloidal projection of parallel flow in the low-field SOL largely cancels with Er × B flow; toroidal rotation is the dominant plasma motion there. The magnitude of the transport-driven poloidal flow is found to be quantitatively consistent with fluctuation-induced radial particle fluxes on the low-field side (LFS), identifying this as the primary drive mechanism. Fluctuation-induced fluxes on the HFS are found to be essentially zero, excluding turbulent inward transport as the mechanism that closes the circulation loop in this region.

Topological characterization of crystalline ice structures from coordination sequences

Topological properties of crystalline ice structures are studied by considering ring statistics, coordination sequences, and topological density of different ice phases. The coordination sequences (number of sites at topological distance k from a reference site) have been obtained by direct enumeration until at least 40 coordination spheres for different ice polymorphs. This allows us to study the asymptotic behavior of the mean number of sites in the k-th shell, Mk, for high values of k: Mk~ak(2), a being a structure-dependent parameter. Small departures from a strict parabolic dependence have been studied by considering first and second differences of the series {Mk} for each structure. The parameter a ranges from 2.00 for ice VI to 4.27 for ice XII, and is used to define a topological density for these solid phases of water. Correlations between such topological density and the actual volume of ice phases are discussed. Ices Ih and Ic are found to depart from the general trend in this correlation due to the large void space in their structures.

Experimentally Based Theoretical Arguments that Unruh’s Temperature, Hawking’s Vacuum Fluctuation and Rindler’s Wedge Are Physically Real

The objective of the present paper is to argue that based on the reality of the observed increased rate of cosmic expansion, Unruh’s temperature, Hawking’s negative vacuum energy and Rindler’s wedge must also be a physical reality. We present first a brief derivation of the missing dark energy density of the universe which is in absolute agreement with the most recent accurate cosmological measurements and observations. The derivation is based upon a Rindler space setting, the associated wedge horizon and Unruh temperature. That way the topological ordinary energy is found to be half of the topological Unruh fluctuation mass m(O) = φ3 multiplied with the square of the topological speed of light c2 = φ2 where φ = 2 /(√5+ 1). This is exactly equal to the area of the spear-like hyperbolic triangular part of the Rindler wedge. The corresponding physical ordinary energy density is thus E(O) = (1/2)( φ3)( φ2) mc2 = (φ5/2)( mc2), where φ5 is Hardy’s probability of quantum entanglement. The topological dark energy density on the other hand is equal half of the topological Kaluza-Klein five dimensional mass m(D) = 5 multiplied with c2 = φ2. This in turn is exactly equal to the circular segment part of the wedge which together with the hyperbolic triangular entangled area forms the complete Lorentzian invariant triangular area of the wedge. Consequently the physical dark energy density which is uncorrelated, i.e. disentangled is given by E(D) = (1/2)(5)( φ2)( mc2) = (5 φ2 /2)( mc2) in full agreement with observation. Adding E(O) and E(D) one finds E(Einstein) = mc2 in full agreement with all our previous derivations. From the above we argue that since measurements, observations and theory have shown the increased expansion to be real and because the present derivation of the same results is based on Rindler’s space and Unruh’s temperature, it follows as a logical necessity that Unruh’s temperature, Hawking’s fluctuation and Rindler’s wedge are all physically real and can be measured, at least in principle.

Topological density of lattice nets

It was shown in a previous paper [Eon (2004). Acta Cryst. A60, 7-18] that the topological density of a periodic net can be calculated directly from its cycles figure, a polytope constructed from those cycles of the quotient graph of the net that are associated with its geodesic lines. It may happen that these lines generate a grid pattern forming a supercell, a phenomenon that was not considered in the former derivation of the formula but is common for lattice nets. An adjustment of the expression is proposed to this effect and applied to the square and hexagonal lattice nets as well as to the 13 families of cubic lattice nets.

Topological analysis of tetraphosphorus oxides (P4O6+n (n = 0–4))

Quantum chemical calculations were used to analyze the chemical bonding and the reactivity of phosphorus oxides (P4O6+n (n = 0-4)). The chemical bonding was studied using topological analysis such as atoms in molecules (AIM), electron localization function (ELF), and the reactivity using the Fukui function. A classification of the P-O bonds formed in all structures was done according to the coordination number in each P and O atoms. It was found that there are five P-O bond types and these are distributed among the five phosphorus oxides structures. Results showed that there is good agreement among the evaluated properties (length, bond order, density at the critical point, and disynaptic population) and each P-O bond type. It was found that regardless of the structure in which a P-O bond type is present the topological and geometric properties do not have a significant variation. The topological parameters electron density and Laplacian of electron density show excellent linear correlation with the average length of P-O bond in each bond type for each structure. From the Fukui function analysis it was possible to predict that from P4O6 until P4O8 the most reactive regions are basins over the P.

Synthesis, molecular structure, and spectral analyses of ethyl-4-[(2,4-dinitrophenyl)-hydrazonomethyl]-3,5-dimethyl-1H-pyrrole-2-carboxylate

Ethyl-4-[(2,4-dinitrophenyl)-hydrazonomethyl]-3,5-dimethyl-1H-pyrrole-2-carboxylate (3) has been newly synthesized by the condensation of ethyl-4-formyl-3,5-dimethyl-1H-pyrrole-2-carboxylate and 2,4-dinitrophenylhydrazine, characterized by FT-IR, 1H NMR, UV–Vis, DART Mass and elemental analysis. The formation of compound (3) and its properties have been evaluated by quantum chemical calculations. The calculated thermodynamic parameters show that the formation reaction of (3) is exothermic and spontaneous at room temperature. The vibrational analysis indicates that (3) forms dimer in the solid state by heteronuclear double hydrogen bonding (N–H···O). Topological parameters electron density (ρ BCP), Laplacian of electron density (∇2 ρ BCP), and total electron energy density (H BCP) at bond critical points (BCP) have been analyzed using “atoms in molecules” (AIM) theory. The interaction energies of dimer formation using DFT and AIM calculations are found to be −14.6509 and −15.5308 kcal/mol, respectively. AIM ellipticity analysis confirms the presence of resonance-assisted hydrogen bonding in dimer. The global electrophilicity index (ω = 5.91 eV) shows that title molecule is a strong electrophile. The local reactivity descriptors Fukui functions (f k + , f k − ), softness (s k + , s k − ), and electrophilicity indices (ω k + , ω k − ) analyses are performed to determine the reactive sites within molecule.

Olefin Metathesis for Effective Polymer Healing via Dynamic Exchange of Strong Carbon–Carbon Double Bonds

In this article, we demonstrate transition-metal-catalyzed olefin metathesis as a simple, effective method for healing polymers via dynamic exchange of strong carbon-carbon double bonds. Upon introducing a very low level of the Grubbs' second-generation Ru metathesis catalyst into cross-linked polybutadiene (PBD) network, the material self-heals effectively at various conditions under moderate pressures. In sharp contrast, catalyst-free control samples with identical network topology and cross-linking density show minimal healing. The healing efficiency of the materials was carefully investigated under different concentrations of the Ru catalyst, compression pressures, and temperatures. It is demonstrated for the first time that a bulk polymer could effectively heal via dynamic covalent bond formation at sub-ambient temperature. The Ru-loaded PBD samples not only heal well with themselves but also with control samples without any catalyst. Furthermore, a completely Ru-free PBD network can heal effectively upon simply applying a very small amount of Ru catalyst only at the fracture surface. The simplicity and effectiveness of this self-healing approach make it potentially applicable to a wide range of olefin-containing polymers.

MAC Protocol Switching: A Novel Tool for Performance Adaptation in Wireless Networks

This paper presents a distributed MAC protocol switching mechanism for maximizing network throughput in the presence of traffic and topology heterogeneity. The key idea behind dynamic MAC switching is for each node to use its local topology and traffic density information to decide the most suitable MAC protocol that can maximize the MAC layer throughout in the neighborhood. A formal MAC switching rule is developed using analytical formulation of the MAC throughput available in the literature. NS2 based simulation experiments demonstrate that with the proposed MAC switching strategy, nodes in a wireless sensor network are able to achieve maximum MAC throughput by adaptively choosing the appropriate MAC protocol in the presence of heterogeneity in terms of data rate and node population.

Hopf fibrations and frustrated matter

Frustrated order appear in different scientific contexts like complex crystals, amorphous materials, liquid crystals, foams and even biological organizations, with scales ranging from the atomic level up to macroscopic scales. In this article, we shall first review several cases where it is possible to release frustration and allows for an unfrustrated structural model by curving the underlying Euclidean space into a positively curved space, the hypersphere S 3. The real Euclidean structure is then analyzed in terms ordered regions interrupted by topological defects, whose presence and density is directly related to the change of curvature from S 3 to R 3. We then focus on a rather fascinating geometrical structure, the Hopf fibration, which can be defined on the hypersphere, and show how this tool is very well suited to describe the defect geometries (both linear, helicoidal and bidimensional) which arises from the decurving procedure.

SU(2) gauge theory of gravity with topological invariants

The most general gravity Lagrangian in four dimensions contains three topological densities, namely Nieh-Yan, Pontryagin and Euler, in addition to the Hilbert-Palatini term. We set up a Hamiltonian formulation based on this Lagrangian. The resulting canonical theory depends on three parameters which are coefficients of these terms and is shown to admit a real SU(2) gauge theoretic interpretation with a set of seven first-class constraints. Thus, in addition to the Newton's constant, the theory of gravity contains three (topological) coupling constants, which might have non-trivial imports in the quantum theory, e.g. in quantum geometry.

Making Insoluble Polymer Networks Malleable via Olefin Metathesis

Covalently cross-linked polymers have many technological applications for their excellent properties, but they suffer from the lack of processability and adaptive properties. We report a simple, efficient method of generating adaptive cross-linked polymers via olefin metathesis. By introducing a very low level of the Grubbs' second-generation Ru metathesis catalyst, a chemically cross-linked polybutadiene network becomes malleable at room temperature while retaining its insolubility. The stress relaxation capability increases with increasing level of catalyst loading. In sharp contrast, catalyst-free control samples with identical network topology and cross-linking density do not show any adaptive properties. This chemistry should offer a possibility to combine the dimensional stability and solvent resistance of cross-linked polymers and the processability/adaptibility of thermoplastics.