Transport of waves in disordered waveguides: A potential model

We study the statistical properties of wave transport in a disordered waveguide. We first derive the properties of a “building block” (BB) of length δL starting from a potential model consisting of thin potential slices. We then find a diffusion equation—in the space of transfer matrices that describe our system—which governs the evolution with the length L of the disordered waveguide of the transport properties of interest. The latter depend only on the mean free paths and on no other property of the slice distribution. The universality that arises demonstrates the existence of a generalized central-limit theorem. We have developed a numerical simulation in which the universal statistical properties of the BB found analytically are first implemented numerically, and then the various BBs are combined to construct the full waveguide. The reported results thus obtained are in good agreement with microscopic calculations, for both bulk and surface disorder.     

Growth of single-walled carbon nanotubes on silicon nanowires

Single-walled carbon nanotubes (SWNTs) have been grown on silicon nanowires (SiNWs) by ethanol chemical vapor deposition (CVD) with Co catalysts. We have found that a surface SiO_x layer of SiNWs is necessary for the formation of active Co catalysts. In fact, the yield of the SWNT/SiNW heterojunctions gradually decreases as the thickness of the surface SiO_x layer decreases. Since thin SiNWs are transparent to an electron beam, the Co nanoparticles on SiNWs can be easily observed as well as SWNTs by TEM. Therefore, the relationship between the diameters of each SWNT and its catalyst nanoparticle has been investigated. The diameters of SWNTs are equal to or slightly smaller than those of the catalyst nanoparticles.     

On the use of response surface methodology to predict and interpret the preferred c-axis orientation of sputtered AlN thin films

This paper deals with experimental design applied to response surface methodology (RSM) in order to determine the influence of the discharge conditions on preferred c-axis orientation of sputtered AlN thin films. The thin films have been deposited by DC reactive magnetron sputtering on Si (1 0 0) substrates. The preferred orientation was evaluated using a conventional Bragg-Brentano X-ray diffractometer (θ-2θ) with the CuKα radiation. We have first determined the experimental domain for 3 parameters: sputtering pressure (2-6 mTorr), discharge current (312-438 mA) and nitrogen percentage (17-33%). For the setup of the experimental design we have used a three factors Doehlert matrix which allows the use of the statistical response surface methodology (RSM) in a spherical domain. A four dimensional surface response, which represents the (0 0 0 2) peak height as a function of sputtering pressure, discharge current and nitrogen percentage, was obtained. It has been found that the main interaction affecting the preferential c-axis orientation was the pressure-nitrogen percentage interaction. It has been proved that a Box-Cox transformation is a very useful method to interpret and discuss the experimental results and leads to predictions in good agreement with experiments.     

Effects of the Ehrlich-Schwoebel potential barrier on the Wolf-Villain model simulations for thin film growth

Wolf-Villain (WV) model is a simple model used to study ideal molecular beam epitaxy (MBE) growth by using computer simulations. In this model, an adatom diffuses instantaneously within a finite diffusion length to maximize its coordination number. We study statistical properties of thin films grown by this model. The morphology of the WV model is found to be kinetically rough with a downhill particle diffusion current. In real MBE growth, however, there are additional factors such as the existence of a potential barrier that is known as the Ehrlich-Schwoebel (ES) barrier. The ES barrier is an additional barrier for an adatom that diffuses over a step edge from the upper to a lower terrace which is known to induce an uphill particle current. We found that with the addition of the ES barrier, the WV-ES model morphology is rough with mound formation on the surface when the barrier is strong enough. To confirm these results, the correlation function is also studied. We find no oscillation in the correlation function in the WV model. For the WV-ES model, the correlation function oscillates. These results confirm that a strong enough ES barrier can cause mound formation on the WV surface in our study.     

Temperature induced asymmetric effects in the surface extended energy loss fine structure of Ni(100)

Electron energy loss spectra have been detected on a Ni(100) surface above the M_{2, 3} core edge at several different temperatures, between 80 and 1300K. We find a strong temperature dependence of the SEELFS signal. In particular we find a strong attenuation of the signal on increasing the temperature (especially the part originating from higher coordination shells). We find also an apparent contraction of the nearest neighbour distance obtained by the Fourier transform technique. We present a model calculation by which we tentatively interpret the apparent contraction as originating from an artifact introduced by the experimental integration limits of the Fourier transform. This in turn is due to an asymmetric pair distribution function of atoms in the surface region.     

Wetting of Heterogeneous Surfaces at the Mesoscopic Scale

We consider the problem of wetting on a heterogeneous wall with mesoscopic defects: i.e., defects of order L ^ε , 0<ε<1, where L is some typical length-scale of the system. In this framework, we extend several former rigorous results which were shown for walls with microscopic defects.^{(10, 11)} Namely, using statistical techniques applied to a suitably defined semi-infinite Ising-model, we derive a generalization of Young's law for rough and heterogeneous surfaces, which is known as the generalized Cassie–Wenzel's equation. In the homogeneous case, we also show that for a particular geometry of the wall, the model can exhibit a surface phase transition between two regimes which are either governed by Wenzel's or by Cassie's law.     

Methods for calculating the desorption rate of an isolated molecule from a surface: Water on MgO(0 0 1)

We present two types of Molecular Dynamics (MD) simulation for calculating the desorption rate of molecules from a surface. In the first, the molecules move freely between two surfaces, and the desorption rate is obtained either by counting the number of desorption events in a given time, or by looking at the average density of the molecules as a function of distance from the surface and then applying transition state theory (TST). In the second, the potential of mean force (PMF) for a molecule is determined as a function of distance from the surface and the desorption rate is obtained by means of TST. The methods are applied to water on the MgO(0 0 1) surface at low coverage. Classical potentials are used so that long simulations can be performed, to minimise statistical errors. The two sets of MD simulations agree well at high temperatures. The PMF method reproduces the 0 K adsorption energy of the molecule to within 5 meV, and finds that the well depth of the PMF is not linear with temperature. This implies the prefactor frequency f in the Polanyi-Wigner equation is a function of temperature, increasing at lower temperatures due to the reduction of the available configuration space associated with an adsorbed molecule compared with a free molecule.     

Investigation of 2-aminoethanethiol as corrosion inhibitor for steel using response surface methodology (RSM)

The inhibition efficiency of 2-aminoethanethiol (2-AEE) has been investigated against steel corrosion in 0.1 M HCl solution. The effect of temperature, pH, and concentration were studied with the help of potentiodynamic measurement, electrochemical impedance spectroscopy, scanning electron microscopy, and atomic absorption spectroscopy techniques. The potential of zero charge (E_pzc) studies showed that the adsorption occurs via ?SH group; the metal surface is positively charged in corrosive test solution. The adsorptive interaction is evaluated, and best correlation was obtained with Langmuir isotherm. 2-AEE was shown to have significant inhibition efficiency against steel corrosion. The response surface methodology was employed to explain the relation between pH, inhibitor concentration, and the efficiency. The regression analysis was realized for development of an equation between independent variables and the output. The success of fitting model was tested with basic statistical arguments, residual and variance analysis, T and F tests, and R ² value. The statistical evaluations showed that the obtained polynomial equation can be successfully used for optimization of applications involving the use of 2-AEE as inhibitor.     

Soliton junctions in the large magnetic flux limit

We study the flux tube junctions in the limit of large magnetic flux. In this limit the flux tube becomes a wall vortex which is a wall of negligible thickness (compared to the radius of the tube) compactified on a cylinder and stabilized by the flux inside. This wall surface can also assume different shapes that correspond to soliton junctions. We can have a flux tube that ends on a wall, a flux tube that ends on a monopole and more generic configurations containing all three of them. In this paper we find the differential equations that describe the shape of the wall vortex surface for these junctions. We will restrict to the cases of cylindrical symmetry. We also solve numerically these differential equations for various kinds of junctions. We finally find an interesting relation between soliton junctions and dynamical systems.     

Disordered clean surfaces and adsorbates investigated with atom-surface scattering

In this paper two different physical situations are considered which can be treated with the same method: a fluid adsorbate (disordered in the x, y plane) and a clean surface with random steps (disordered in the z direction). The hard corrugated wall model is used in the eikonal approximation; the differences between the two cases arise only from the different statistical properties of the two physical situations. The differential scattering probability is evaluated. For the fluid adsorbate the latter splits into a coherent (purely specular) contribution and an incoherent one (which is, in fact, weakly inelastic and related to classical diffusion on the surface). For stepped “rough” surfaces only incoherent scattering is present and the differential scattering probability for hexagonal lattices is given.     

The Kolkata Paise Restaurant problem and resource utilization

We study the dynamics of the “Kolkata Paise Restaurant problem”. The problem is the following: In each period, N agents have to choose between N restaurants. Agents have a common ranking of the restaurants. Restaurants can only serve one customer. When more than one customer arrives at the same restaurant, one customer is chosen at random and is served; the others do not get the service. We first introduce the one-shot versions of the Kolkata Paise Restaurant problem which we call one-shot KPR games. We then study the dynamics of the Kolkata Paise Restaurant problem (which is a repeated game version of any given one shot KPR game) for large N. For statistical analysis, we explore the long time steady state behavior. In many such models with myopic agents we get under-utilization of resources, that is, we get a lower aggregate payoff compared to the social optimum. We study a number of myopic strategies, focusing on the average occupation fraction of restaurants.     

An additional kind of nonlinear s-polarized surface plasmon polaritons

We have explored the dispersion relations for s-polarized surface plasmon polaritons guided by a metal film sandwiched between a linear substrate and a cladding with an intensity-dependent refractive index. In contrast to a previous paper we found surface plasmon polaritons for this configuration which exhibit a definite power threshold and a limited range for permitted propagation constants as well.     

Theoretical studies of electronic states and phonon modes on the TiC(0 0 1)(1 × 1) surface

We present a comprehensive picture of structural and electronic properties of the TiC(0 0 1)(1 × 1) surface. Our investigations are based on first-principles calculations within the local-density approximation of the density-functional theory. Good agreement has been observed between our calculation and experimental data for the atomic geometry of the surface. In particular, the calculated bond lengths between the first-layer C and the second-layer Ti (d_1C-2Ti = 2.188 Å) and between the first-layer Ti and the second-layer C (d_1Ti-2C = 2.031 Å) are in good agreement with the corresponding experimental values of 2.25 Å and 2.14 Å, respectively. We have also identified surface electronic states and provided clear support for previously available photoemission measurements. We have further calculated surface phonon modes at the zone centre and at the zone-edge point X using a linear response scheme based on the ab initio pseudopotential method. Our calculated surface phonon results are in excellent agreement with electron energy loss spectroscopy results.     

Statistical mechanics of two-dimensional point vortices: relaxation equations and strong mixing limit

We complement the literature on the statistical mechanics of point vortices in two-dimensional hydrodynamics. Using a maximum entropy principle, we determine the multi-species Boltzmann-Poisson equation and establish a form of Virial theorem. Using a maximum entropy production principle (MEPP), we derive a set of relaxation equations towards statistical equilibrium. These relaxation equations can be used as a numerical algorithm to compute the maximum entropy state. We mention the analogies with the Fokker-Planck equations derived by Debye and Hückel for electrolytes. We then consider the limit of strong mixing (or low energy). To leading order, the relationship between the vorticity and the stream function at equilibrium is linear and the maximization of the entropy becomes equivalent to the minimization of the enstrophy. This expansion is similar to the Debye-Hückel approximation for electrolytes, except that the temperature is negative instead of positive so that the effective interaction between like-sign vortices is attractive instead of repulsive. This leads to an organization at large scales presenting geometry-induced phase transitions, instead of Debye shielding. We compare the results obtained with point vortices to those obtained in the context of the statistical mechanics of continuous vorticity fields described by the Miller-Robert-Sommeria (MRS) theory. At linear order, we get the same results but differences appear at the next order. In particular, the MRS theory predicts a transition between sinh and tanh-like ω ? ψ relationships depending on the sign of Ku ? 3 (where Ku is the Kurtosis) while there is no such transition for point vortices which always show a sinh-like ω ? ψ relationship. We derive the form of the relaxation equations in the strong mixing limit and show that the enstrophy plays the role of a Lyapunov functional.     

Influence of subcutaneous fat in surface heating of ultrasonic diagnostic transducers

The transducers of diagnostic ultrasonic equipment generate undesired local heating at the applied part of the transducer surface. The assessment of this heating is fundamental in warranting patient safety. On the standard IEC 60601-2-37, methods have been established for the reliable measurement of heating, where three tissue models based on tissue-mimicking materials are recommended: soft tissue mimic only, bone mimic close to the surface of soft tissue, and skin mimic at the surface of soft tissue. In the present work, we compared the last-mentioned tissue model with a new one using a layer of porcine subcutaneous fat inserted between the soft tissue and skin-mimicking materials. We verify significant statistical differences between models, with the average temperature rise measured for the tests without subcutaneous fat at 6.7 °C ± 1.7 °C and for the ones with subcutaneous fat at 8.9 °C ± 1.8 °C (k = 2; p = 0.95). For each model, the procedure was performed 10 times in repeatability conditions of measurement. It has been suggested that the influence of subcutaneous fat for external transducers heating evaluation should be considered, as the presence of many millimeters of subcutaneous fat is a common condition in patients. Otherwise, the transducer surface heating and, therefore, the risk to the patient may be underestimated.     

The conformation of adsorbed polyacrylamide and derived polymers

We have studied the adsorption of different polyacrylamide derivatives in water on freshly cleaved mica surfaces. Using the potential of measuring force versus distance profiles with an atomic force microscope (AFM), we investigate the conformation and the loop distribution of adsorbed chains. In particular, we explain that (i) the loop distribution of the polyacrylamide homopolymer can be described from scaling laws arguments, (ii) the loop distribution of statistical copolymers should be a signature of the distribution of the monomers along the chain backbone, and (iii) hydrophobically modified polyacrylamide copolymers form surface gels whose growing kinetics can be studied by AFM. Our results also show that the co-operative effect of H-bonding can give much larger adhesion that ionic association.     

Replica Symmetry Breaking Condition Exposed by Random Matrix Calculation of Landscape Complexity

We start with a rather detailed, general discussion of recent results of the replica approach to statistical mechanics of a single classical particle placed in a random N(?1)-dimensional Gaussian landscape and confined by a spherically symmetric potential suitably growing at infinity. Then we employ random matrix methods to calculate the density of stationary points, as well as minima, of the associated energy surface. This is used to show that for a generic smooth, concave confining potentials the condition of the zero-temperature replica symmetry breaking coincides with one signaling that both mean total number of stationary points in the energy landscape, and the mean number of minima are exponential in N. For such systems the (annealed) complexity of minima vanishes cubically when approaching the critical confinement, whereas the cumulative annealed complexity vanishes quadratically. Different behaviour reported in our earlier short communication (Fyodorov et al. in JETP Lett. 85:261, 2007) was due to non-analyticity of the hard-wall confinement potential. Finally, for the simplest case of parabolic confinement we investigate how the complexity depends on the index of stationary points. In particular, we show that in the vicinity of critical confinement the saddle-points with a positive annealed complexity must be close to minima, as they must have a vanishing fraction of negative eigenvalues in the Hessian.     

Combining Sparse and Dense Features to Improve Multi-Modal Registration for Brain DTI Images

A new solution to overcome the constraints of multimodality medical intra-subject image registration is proposed, using the mutual information (MI) of image histogram-oriented gradients as a new matching criterion. We present a rigid, multi-modal image registration algorithm based on linear transformation and oriented gradients for the alignment of T2-weighted (T2w) images (as a fixed reference) and diffusion tensor imaging (DTI) (b-values of 500 and 1250 s/mm²) as floating images of three patients to compensate for the motion during the acquisition process. Diffusion MRI is very sensitive to motion, especially when the intensity and duration of the gradient pulses (characterized by the b-value) increases. The proposed method relies on the whole brain surface and addresses the variability of anatomical features into an image stack. The sparse features refer to corners detected using the Harris corner detector operator, while dense features use all image pixels through the image histogram of oriented gradients (HOG) as a measure of the degree of statistical dependence between a pair of registered images. HOG as a dense feature is focused on the structure and extracts the oriented gradient image in the x and y directions. MI is used as an objective function for the optimization process. The entropy functions and joint entropy function are determined using the HOGs data. To determine the best image transformation, the fiducial registration error (FRE) measure is used. We compare the results against the MI-based intensities results computed using a statistical intensity relationship between corresponding pixels in source and target images. Our approach, which is devoted to the whole brain, shows improved registration accuracy, robustness, and computational cost compared with the registration algorithms, which use anatomical features or regions of interest areas with specific neuroanatomy. Despite the supplementary HOG computation task, the computation time is comparable for MI-based intensities and MI-based HOG methods.     

X-ray diffraction analysis of the silicon (111) surface during alkaline etching

We present a surface X-ray diffraction determination of the silicon (111)-liquid interface structure during alkaline etching. Preparation of an atomically smooth surface was realized by an in-situ procedure using an aqueous NH₄F solution devoid of oxygen. Using diluted aqueous potassium hydroxide (KOH) and ammonium fluoride (NH₄F) etchant, we have observed that the crystal surface is hydrogen terminated and is not reconstructed at open circuit potential. In addition, a partial liquid ordering of two water layers on top of the crystal surface was found, indicating a weak interaction with the hydrophobic, hydrogen terminated surface. We have followed in-situ the development of the oxide layer by a birth and spread mechanism during anodic passivation of the silicon surface.