Wada boundary bifurcations induced by boundary saddle–saddle collision

In this letter, a Wada boundary bifurcation (WBB) induced by a boundary saddle touching another boundary saddle is first found through the study of a forced damped pendulum. The WBB can be quantitatively described by the change both in the number of basins involved and in the geometrical size of the boundary. We perceive the manifold structures of the two saddles, that is, a pre-existence of heteroclinic crossing and the other nearly forming heteroclinic tangency exist before the WBB. So we schematically construct the equivalent topological structure of the manifolds of arbitrary two saddles, and rigorously prove two theorems that indicate the existence of the heteroclinic tangency and thus generically confirm the mechanism of such WBB.     

Grain boundary segregation diagrams of α-iron

Based on thermodynamic analysis of interfacial segregation, the segregation enthalpy H ^o of a solute I in a given matrix was found to depend linearly on two mutually independent terms reflecting the type of interface and the solid solubility limit X _infI ^sup* at temperature T and can be written as In this equation, the structural dependence of interfacial segregation is contained in H ^*() which corresponds to the extrapolated segregation enthalpy of a solute with unlimited solubility in the matrix. The product [Tln(X _infI ^sup* )] is essentially constant with temperature, and can therefore be obtained from data for maximum solid solubility, [Tln(X _infI ^sup* )]_max. The parameter v>0 represents the relationship between the activity a _infI ^sup* of a solute at the bulk solid solubility limit in a given matrix and X _infI ^sup* , a _infI ^sup* =(X _infI ^sup* ) ^v , and is characteristic for the matrix. Using recent experimental data for silicon, phosphorus, and carbon segregation at well-characterized grain boundaries in oriented bicrystals of -iron, the averaged value was determined. Values of H ^*() range from -8 kJ/mol (general grain boundaries) up to +8 kJ/mol (special grain boundaries). These values are discussed and used for a more precise and generalized construction of grain boundary segregation diagrams of -iron.     

On the boundary slip of fluid flow

For hundreds of years, in all the textbooks of classical fluid mechanics and lubrica- tion mechanics it is assumed that there was no wall slip (boundary slip) at a liquid-solid interface, i.e. no relative motion between liquid and solid at the interface. This is the no-slip boundary condition. It has been widely applied to engineering and experiments and to almost all the rheology or viscosity measurements of fluids. Rheology is one of the most important bases for fluid mechanics and lubricati…     

Grain boundary chemistry and grain boundary dislocations in bulk YBa2Cu3O7-δ

We report the results of our microchemical analyses of low- large-angle grain boundaries in bulk YBa₂Cu₃O_7- using nanoprobe energy-dispersive-X-ray spectroscopy (EDX) and electron-energy-loss spectroscopy (EELS). We observed periodic variation in the concentration of Cu along the boundaries, and oxygen depletion at the boundaries. We found that the chemistry of the grain boundary is very sensitive to grain boundary dislocations (GBDs), while, in turn, the configuration of the GBDs is very sensitive to the boundary misorientation and the boundary plane normal. The strain field associated with closely spaced GBDs reduced the density of mobile holes at the boundary, which is expected to be detrimental to the superconducting properties of the boundary. The possible structural transition of the grain boundaries from an oxygen-deficient state to a fully oxygenated state near a coincidence orientation is discussed, based on the reduction of the elastic strain energy of the boundaries.     

Crack–grain boundary interactions in zinc bicrystals

In polycrystalline materials that fail by transgranular cleavage, it is known that crystallographic misorientation of preferred fracture planes across grain boundaries can provide crack growth resistance; despite this, the micromechanisms associated with crack transmission across grain boundaries and their role in determining the overall fracture resistance are not well understood. Recent studies on diverse structural materials such as steels, aluminum alloys and intermetallics have shown a correlation between fracture resistance and the twist component of grain misorientation. However, the lack of control over the degree and type of misorientation in experimental studies, combined with a dearth of analytical and computational investigations that fully account for the three-dimensional nature of the problem, have precluded a systematic analysis of this phenomenon. In this study, this phenomenon was investigated through in situ crack propagation experiments across grain boundaries of controlled twist misorientation in zinc bicrystals. Extrinsic toughening mechanisms that activate upon crack stagnation at the grain boundary deter further crack propagation. The mechanical response and crack growth behavior were observed to be dependent on the twist angle, and several accommodation mechanisms such as twinning, strain localization and slip band blocking contribute to fracture resistance by competing with crack propagation. Three-dimensional finite element analyses incorporating crystal plasticity were performed on a stagnant crack at the grain boundary that provide insight into crack-tip stress and strain fields in the second grain. These analyses qualitatively capture the overall trends in mechanical response as well as strain localization around stagnant crack-tips.     

The dominant deformation mechanism of nanocrystalline materials with the finest grains: grain boundary sliding or grain boundary migration?

We report an efficient room-temperature synthesis of Au nanoparticles (NPs) using carbon dots (C-dots) as mediator in poly(ethylene glycol). The synthesis does not require any irradiation or heating for the reduction of the metal precursor and it yields smaller sized particles of ~15 nm, mostly octahedron in shape. The effect of varying concentrations of the Au precursor and C-dots on the synthesis was studied, which demonstrated the variation in particle size and shape with change in either the precursor or C-dots concentration. Time-resolved absorbance study for the synthesis of Au NPs showed the sigmoidal behavior for the autocatalytic growth having the lagging phase of induction period. The optimum concentration of the precursor and the C-dots were determined for the synthesis of well-dispersed Au NPs. The stability of the prepared Au NPs was also determined, showing that at optimum concentration of the precursor and C-dots, the particles were stable and did not precipitate for several days.     

Grain boundary segregation and relaxation in nano-grained polycrystalline alloys

The present study carries out systematic thermodynamics analysis of Grain Boundary(GB)segregation and relaxation in NanoGrained(NG)polycrystalline alloys.GB segregation and relaxation is an internal process towards thermodynamic equilibrium,which occurs naturally in NG alloys without any applied loads,causes deformation and generates internal stresses.The analysis comprehensively investigates the multiple coupling effects among chemical concentrations and mechanical stresses in GBs and grains.A hybrid approach of eigenstress and eigenstrain is developed herein to solve the multiple coupling problem.The analysis results indicate that the GB stress and grain stress induced by GB segregation and relaxation can be extremely high in NG alloys,reaching the GPa level,which play an important role in the thermal stability of NG alloys,especially via the coupling terms between stress and concentration.The present theoretic analysis proposes a novel criterion of thermal stability for NG alloys,which is determined by the difference in molar free energy between a NG alloy and its reference single crystal with the same nominal chemical composition.If the difference at a temperature is negative or zero,the NG alloy is thermal stable at that temperature,otherwise unstable.     

The QCD phase boundary from quark–gluon dynamics

We study one-flavor QCD at finite temperature and chemical potential using the functional renormalization group. We discuss the chiral phase transition in QCD and its order with its underlying mechanism in terms of quarks and gluons and analyze the dependence of the phase-transition temperature on small quark chemical potentials. Our result for the curvature of the phase boundary at small quark chemical potential relies on only a single input parameter, the value of the strong coupling at the Z mass scale.     

Calculation of multi frequency of Helmholtz boundary integral equation

The method using series expansion is presented, and the wavenumber is separated from fundamental solution of Helmholtz boundary element equation, then the system matrices dependent of wavenumber are the matrices series associated with wavenumber, and the astringency of the method is proved. The numerical results show that combined with the CHIEFmethod, the SECHIEF (Series Expansion Combined Helmholtz Integral Equation Formulation) method can not only provide uniqueness of solution and reduce the computational time but also give accurate results under the coarse elements.     

Charge transport across the metal–polymer film boundary

Thin polyaniline films were fabricated by thermal vacuum evaporation from a Knudsen effusion cell. The conducting properties of films synthesized under different evaporation conditions were studied. The enhancement of the emission capacity of a wolfram tip coated with a polyaniline film of a nanometer thickness was demonstrated experimentally. A model of the discovered effect was proposed. The obtained Fowler–Nordheim current–voltage characteristics were used to estimate the change in the electronic work function occurring when a thin film is deposited on the tip surface. The effective temperature of electrons emitted from the polyaniline film was determined based on the results of analysis of energy distributions, and the specific features of charge transport in the metal–polyaniline–vacuum system were examined. A model of energy bands of the metal–polymer film contact was also constructed.     

One-loop surface tension on a boundary inλφ 4 theory

We calculate quantum corrections to the vacuum energy in ⁴ theory with a tachyonic mass term in a half space, where the scalar field is required to satisfy the Dirichlet boundary condition on the surface. It is found that the one-loop self-energy diagram includes a finite energy portion, representing a repulsive surface tension on the boundary.     

Padé approximation in time-domain boundary conditions of porous surfaces

Formulation and implementation of time-domain boundary conditions (TDBCs) at the surface of a reactive porous material are made challenging by the slow decay, complexity, or noncausal nature of many commonly used models of porous materials. In this paper, approaches are described that improve computational efficiency and enforce causality. One approach involves approximating the known TDBC for the modified Zwikker-Kosten impedance model as a summation of decaying exponential functions. A second approach, which can be applied to any impedance model, involves replacing the characteristic admittance with its Padé approximation. Then, approximating fractional derivatives with decaying exponentials, a causal and recursive TDBC is formulated.     

Maxwell–Wagner polarization in grain boundary segregated NiCuZn ferrite

The present work investigates the polarization response in polycrystalline Ni_0.9−yCu_yZn_0.1Fe_1.98O_4−δ (y = 0, 0.1, 0.2, 0.3, 0.4, 0.5) ferrite synthesized by solid–state reaction method. X-ray diffraction analysis confirmed cubic spinel phase formation in the calcined samples. Sintered samples contain a continuous network of CuO-rich segregation along the grain boundaries for y ≥ 0.2. Dielectric spectra showed a relaxation peak for y ≥ 0.2 in the frequency range of 1 kHz–1 MHz. This relaxation has been explained based on Maxwell–Wagner polarization considering two-layer model in connection with two heterogeneous dielectric media.     

T-duality simplifies bulk–boundary correspondence: the noncommutative case

We state and prove a general result establishing that T-duality, or the Connes–Thom isomorphism, simplifies the bulk–boundary correspondence, given by a boundary map in K-theory, in the sense of converting it to a simple geometric restriction map. This settles in the affirmative several earlier conjectures of the authors and provides a clear geometric picture of the correspondence. In particular, our result holds in arbitrary spatial dimension, in both the real and complex cases, and also in the presence of disorder, magnetic fields, and H-flux. These special cases are relevant both to string theory and to the study of the quantum Hall effect and topological insulators with defects in condensed matter physics.     

Domain boundary engineering – recent progress and many open questions

Some domain boundaries contain functionalities which do not exist in the bulk. Typical examples are (super-) conducting twin walls in WO₃, highly conducting walls in BiFeO₃ and in structural interfaces between SrTiO₃ and LaAlO₃, and ferroelectric walls in CaTiO₃. The emerging field of ‘Domain Boundary Engineering’ endeavors to generate such functional interfaces in a multitude of materials for applications in device materials. Some of the recent successes are reviewed together with suggestions for further research.     

Plasmonic wave propagation along a magnetized plasmon–dielectric boundary

The emphasis of this paper is on investigation of the TM/TE depolarization along a magnetized surface. In this regard, initially, the wave equation with appropriate boundary conditions is solved for the propagation constant of the wave along the interface. Next, in order to investigate the electromagnetic field TM/TE depolarization along a linear magnetoplasmon–dielectric interface, coupled partial differential equations are derived for the amplitudes of the TE and TM polarized fields along the surface. These equations are then solved using the Fourier transform and 4th order Runge–Kutta methods and the envelopes of the electric field are obtained. The dependency of the propagation constants of the slow and fast modes on the frequency and magnitude of DC magnetic bias field is investigated. A discussion of TE mode deflection is also provided.     

DNS of compressible turbulent boundary layer over a blunt wedge

Wall turbulence is more complicated than free turbulence, and the direct numerical simulation (DNS) of wall turbulence is more difficult. In recent years, most of DNS cases for wall turbulence are simplified by using temporal mode, where streamwise pe- riodic boundary condition is imposed. In temporal mode, spatial transition will be con- sidered as an analogue of time-evolving transition. For the channel turbulence, an equivalent body force can substitute for the mean gradient of pressure, …