Narrow Results

Point contact tunneling data are reported in a multilayered high-T_c cuprate (Cu,C)Ba₂Ca₃Cu₄O_12+δ with T_c = 117 K. The tunneling spectra in the superconducting state (T ≪ T_c) display spectral features such as well-defined superconducting gap peak at ±Δ as well as dip-hump structures beyond the peaks. In some cases, the spectra with two-gaps have been observed, indicating the coexistence of two inequivalent superconducting layers. The statistical distribution of superconducting gap magnitude suggests two distinct kinds of superconducting gaps that may originate from two inequivalent CuO₂ planes, a characteristics of multilayered cuprates with n ≥ 3.

The traffic flow on a 3-lane highway is investigated using a cellular automaton method. Two different kinds of vehicles, cars and trucks, with different driving behaviors are presented on the highway. It is found that in the high density region, a control scheme requiring passing from the inner lane will enhance the traffic flow; while restricting the trucks to the outer lane will enhance the flow in the low density region and also has the benefit of suppressing the unnecessary lane-changing rate.

Spatial variation of low temperature tunneling spectrum on atomic scale was examined on the slightly underdoped Bi2212 sample (T_c~74K, p~0.12) by using a STM/STS technique. We observed a V-shaped gap with sharp coherence peaks, which is expected for d-wave superconductors, over the distance of ~18 nm and no other kind of gap. The spatial variation of gap size Δ₀ is small, ranging from 41 to 53 meV. These results indicate that the superconductivity takes place rather homogeneously in the slightly underdoped sample.

A theoretical formalism which can be combined with any hard sphere density functional approximations (DFA) to construct DFA for non-hard sphere fluids with a hard or soft core subjected to diverse external potentials is proposed. To show validity and power of the present formalism, we employ a simple weighted density approximation as an illustrating example. It is found that the resultant DFA for Lennard–Jones fluid under influences of diverse extenal potentials is in generally satisfactory agreement with corresponding simulational results even though the co-existence bulk fluid in the particle reservoir with which the non-uniform fluid under consideration is connected, is situated at "dangerous" regions. The significance of the present formalism lies in that it can be combined with any other hard sphere DFAs to construct DFAs for any non-hard sphere fluids with a hard or soft core.

A theoretical way is proposed, by which any hard sphere density functional approximation (DFA) can be applied to non-hard sphere fluids for the calculation of density profile in the framework of density functional theory (DFT). Used as examples, the present formalism is combined respectively with two recently proposed hard sphere DFAs to predict the density profile of Lennard–Jones (LJ) fluid, hard core square well (SW) fluid and penetrable potenial fluid subjected to diverse external fields. Extensive comparison between theoretical predictions and corresponding simulation results shows that the present theoretical way, when combined with an accurate hard sphere DFA, can perform well for calculating the density profile of the non-uniform fluids of the above mentioned potentials. Concretely speaking, for LJ and hard core SW fluid, even a less accurate FEDFA is sufficient, while for extreme potential such as the penetrable potenial, a more accurate adjustable parameter free version of LTDFA is needed to combine with the present theoretical way to predict density profile satisfactorily. The advantage of the proposed theoretical way is that the resultant DFA is applicable to both subcritical and supercritical temperature cases, thereby overcoming the disadvantages of previous two categories of DFT approach.

We observed the distribution of the superconducting gap in Bi₂Sr_2-xLa_xCuO_6+δ (Bi2201-La) by scanning tunneling spectroscopy at x = 0.2 (over doped), 0.4 (optimally doped) and 0.6 (under doped). The superconducting gap was spatially distributed in all samples. As the carrier concentration is reduced, the distribution became much broader and the mean value of superconducting gap, Δ_mean increased. We found that the distribution and Δ_mean in Bi2201-La grew more rapidly than in Bi₂Sr₂CaCu₂O_8+δ with decreasing the carrier concentration.

To understand several peculiar features of d-wave superconductors such as the cuprates, we have studied a two-dimensional tight-binding (extended Hubbard) model in which the electrons interact with a potential which is attractive at nearest neighbor distance and repulsive elsewhere. Such a model is designed to produce d-wave superconductivity. It also yields antiferromagnetism and phase separation. In the two-phase region, due to vanishing compressibility the system can be easily rendered inhomogeneous by weak perturbations. Thus inhomogeneous superconductivity is a likely consequence of d-wave pairing. In addition to inhomogeneity the model also reproduces a phase diagram strikingly similar to the one observed in the cuprates. As such it throws some light on the nature of the pseudogap state.

To understand the interplay of d-wave superconductivity and antiferromagnetism, we consider a two-dimensional extended Hubbard model with nearest neighbor attractive interaction. The Hamiltonian is solved in the mean field approximation on a finite lattice. In the impurity-free case, the minimum energy solutions show phase separation as predicted previously based on free energy argument. The phase separation tendency implies that the system can be easily rendered inhomogeneous by a small external perturbation. Explicit solutions of a model including weak impurity potentials are indeed inhomogeneous in the spin-density-wave and d-wave pairing order parameters. Relevance of the results to the inhomogeneous cuprate superconductors is discussed.

Symmetric and anti-symmetric trapped modes in a cylindrical tube with a segment of higher density are studied. The problem is reduced to an eigenvalue problem of the spatial Helmholtz equation subject to vanishing Dirichlet boundary condition in the cylindrical coordinate system. Through the domain decomposition method and matching technique, multiple frequency parameters are determined by solving the characteristic equation, and the corresponding n-fold periodic trapped modes can be constructed. It is found that in addition to the fundamental mode, the second- and higher-order trapped modes exist, which depend on the density ratio and length of the inhomogeneity. The local inhomogeneity leads to a decrease of the cutoff frequencies of the homogeneous tube and the corresponding vibration mode is localized near the inhomogeneous segment.

Heterogeneity in the electrical activity across the ventricular wall might result from transmural differences in myocardial membrane ionic current densities. Computational models of endo- and epi-cardial action potentials of guinea-pig myocytes were developed, assuming transmural differences in the ionic current densities and kinetics of i_Kr and i_Ks. The cell models were able to reproduce the characteristics of action potentials of endo and epi cells. One- and two-dimensional models of ventricular tissue were also developed to study the effects of transmural heterogeneity on the propagation of excitation waves across the ventricle wall. It was shown that intercellular coupling reduces the transmural heterogeneity across the ventricle wall.

A detailed study of higher-dimensional quasi-spherical gravitational collapse with radial and tangential stresses has been done and the role of initial data, anisotropy and inhomogeneity has been investigated in determining the end state of collapse. By linear scaling the initial data set and the area radius, it is found that the dynamics of quasi-spherical collapse remains invariant. In other words, the linear transformation identifies an equivalence class of data sets for which physical parameters like density, pressures (radial and tangential), shear remain invariant and the final state of collapse is identical (black hole or naked singularity). Finally, the role of anisotropy and inhomogeneity has been studied by proving some propositions.

Current widespread use of ecological terms such as variability, heterogeneity and homogeneity is misleading and prevents ecologists from reaching a terminological consensus on what is meant when discussing these concepts, in particular with regard to the descriptor 'heterogeneous.' We propose the use of 'inhomogeneity' to define patterns or processes exhibiting a scale-dependent structure, whether spatial or temporal. Thus, the concept of 'inhomogeneity' can be regarded as a structural ecological entity. A descriptor exhibiting different kinds of inhomogeneity, either spatially or temporally, will then be qualified as being heterogeneous. The terminological consensus introduced here in the particular frame of ecological sciences is finally discussed and generalized to the actual scientific thought process.

Experiments showed that bacterial biofilms are heterogeneous, for example, the density, the diffusion coefficient, and mechanical properties of the biofilm are different along the biofilm thickness. In this paper, we establish a multi-layer composite model to describe the biofilm mechanical inhomogeneity based on unified multiple-component cellular automaton (UMCCA) model. By using our model, we develop finite element simulation procedure for biofilm tension experiment. The failure limit and biofilm extension displacement obtained from our model agree well with experimental measurements. This method provides an alternative theory to study the mechanical inhomogeneity in biological materials.

This paper deals with the interaction between a circular piezoelectric inhomogeneity (a circular piezoelectric fiber sensor) and a symmetrically branched crack. The piezoelectric inhomogeneity is embedded in a nonpiezoelectric, elastic matrix with a symmetrically branched crack near the inhomogeneity. The matrix is under a far field in-plane uniform tensile stress and an anti-plane electric field. By using the solution of a single dislocation interacting with an inhomogeneity as Green's function, the main crack and its two symmetrical branches are simulated by continuously distributed edge dislocations. The formulation results in a group of singular integral equations (SIEs). Through solving the singular integral equations numerically, the unknown distributed dislocation density functions can be obtained, and both the Mode I and Mode II stress intensity factors at the branch tips are thus evaluated. The influence of materials constants, geometrical configurations, as well as the far field electric and mechanical loading on the interaction between the branched crack and the piezoelectric inhomogeneity is discussed in detail. As the derivation procedure is very tedious, the analytical results obtained are verified by finite element computation.

This work develops a semi-analytic solution for multiple inhomogeneous inclusions of arbitrary shape and cracks in an isotropic infinite space. The solution is capable of fully taking into account the interactions among any number of inhomogeneous inclusions and cracks which no reported analytic or semi-analytic solution can handle. In the solution development, a novel method combining the equivalent inclusion method (EIM) and the distributed dislocation technique (DDT) is proposed. Each inhomogeneous inclusion is modeled as a homogenous inclusion with initial eigenstrain plus unknown equivalent eigenstrain using the EIM, and each crack of mixed modes I and II is modeled as a distribution of edge climb and glide dislocations with unknown densities. All the unknown equivalent eigenstrains and dislocation densities are solved simultaneously by means of iteration using the conjugate gradient method (CGM). The fast Fourier transform algorithm is also employed to greatly improve computational efficiency. The solution is verified by the finite element method (FEM) and its capability and generality are demonstrated through the study of a few sample cases. This work has potential applications in reliability analysis of heterogeneous materials.

General hyperbolic systems of balance laws with inhomogeneous flux and source are studied. Global existence of entropy weak solutions to the Cauchy problem is established for small BV data under appropriate assumptions on the decay of the flux and the source with respect to space and time. There is neither a hypothesis about equilibrium solution nor about the dependence of the source on the state vector as previous results have assumed.

A numerical model based on the dual reciprocity boundary element method (DRBEM) for studying the transient magneto-thermo-viscoelastic stresses in a nonhomogeneous anisotropic solid subjected to a heat source is presented. The formulation is tested through its application to the problem of a solid placed in a constant primary magnetic field acting in the direction of the z-axis and rotating about this axis with a constant angular velocity. In the case of plane deformation, a numerical scheme for the implementation of the method is presented and the numerical computations are carried out for the temperature, displacement components and stress components. The validity of DRBEM is examined by considering a magneto-thermo-viscoelastic solid occupies a rectangular region and good agreement is obtained with existent results. The results obtained are presented graphically to show the effects of inhomogeneity and heat source on the temperature, displacement components and thermal stress components.

The present paper is devoted to study the Love wave propagation in a fiber-reinforced medium laying over a nonhomogeneous half-space. The upper layer is assumed as reinforced medium and we have taken exponential variation in both rigidity and density of lower half-space. As Mathematical tools the techniques of separation of variables and Whittaker function are applied to obtain the dispersion equation of Love wave in the assumed media. The dispersion equation has been investigated for three different cases. In a special case when both the media are homogeneous our computed equation coincides with the classical equation of Love wave. For graphical representation, we used MATLAB software to study the effects of reinforced parameters and inhomogeneity parameters. It has been observed that the phase velocity increases with the decreases of nondimensional wave number. We have also seen that the phase velocity decreases with the increase of reinforced parameters and inhomogeneity parameters. The results may be useful to understand the nature of seismic wave propagation in fiber reinforced medium.

This paper provides a closed form solution for dissimilar elliptical inclusion in plane elasticity. A dissimilar elliptical inclusion is embedded in the infinite matrix with different elastic properties. The infinite matrix is applied by the constant remote loading. Complex variable method is used and two sets of the complex potentials are assumed in the analysis. One set is used for the matrix portion, and other for the inclusion portion. Catching the idea from the eigenstrain problem, we can assume the stresses in the inclusion to be constant. From the continuity conditions for stresses and displacements along the interface, we can get the two sets of the complex potentials in a closed form. In the analysis, an adequate form of the complex potential defined in the elliptical inclusion portion is analyzed in detail.

In this paper, the effect of initial stress on the propagation of Love waves in a layered structure with a thin piezoelectric film bonded perfectly to an elastic substrate has been investigated. General dispersion equations, describing the properties of Love waves in both cases, electrically open case and electrically shorted case of the piezoelectric layer, have been obtained. The effects of inhomogeneity parameters in the substrate and the initial stress in both, the layer and the substrate on the phase velocity of Love waves, are analyzed and presented graphically. The analytical method and obtained results may find applications for designing the resonators and sensors.