Finite volume evolution Galerkin method for hyperbolic conservation laws with spatially varying flux functions

We present a generalization of the finite volume evolution Galerkin scheme [M. Lukacova-Medvid'ova,J. Saibertov'a, G. Warnecke, Finite volume evolution Galerkin methods for nonlinear hyperbolic systems, J. Comp. Phys. (2002) 183 533-562; M. Luacova-Medvid'ova, K.W. Morton, G. Warnecke, Finite volume evolution Galerkin (FVEG) methods for hyperbolic problems, SIAM J. Sci. Comput. (2004) 26 1-30] for hyperbolic systems with spatially varying flux functions. Our goal is to develop a genuinely multi-dimensional numerical scheme for wave propagation problems in a heterogeneous media. We illustrate our methodology for acoustic waves in a heterogeneous medium but the results can be generalized to more complex systems. The finite volume evolution Galerkin (FVEG) method is a predictor-corrector method combining the finite volume corrector step with the evolutionary predictor step. In order to evolve fluxes along the cell interfaces we use multi-dimensional approximate evolution operator. The latter is constructed using the theory of bicharacteristics under the assumption of spatially dependent wave speeds. To approximate heterogeneous medium a staggered grid approach is used. Several numerical experiments for wave propagation with continuous as well as discontinuous wave speeds confirm the robustness and reliability of the new FVEG scheme.

Spatially dependent zero-frequency response functions and correlation functions in the Kondo model

We present the details of a formalism for calculating spatially varying zero-frequency response functions and equal-time correlation functions in models of magnetic and mixed-valence impurities of metals. The method is based on a combination of perturbative, thermodynamic scaling theory [H. R. Krishna-murthy and C. Jayaprakash, Phys. Rev. B 30, 2806 (1984)] and a nonperturbative technique such as the Wilson renormalization group. We illustrate the formalism for the spin-1/2 Kondo problem and present results for the conduction-spin-density�impurity-spin correlation function and conduction-electron charge density near the impurity. We also discuss qualitative features that emerge from our calculations and discuss how they can be carried over to the case of realistic models for transition-metal impurities.

Laminar flow of a suspension in a curved pipe with varying curvature

The laminar flow of a fairly concentrated suspension (in which the volume fraction Z of the solid particles < 0.4) in a spatially varying periodically curved pipe has been examined numerically. Unlike the case of interacting suspension flows, the particles are found to flow in a well-mixed fashion, altering both the axial and circumferential velocities and consequently the fluid flux in the tube, depending on their diffusivity and inertia. The magnitude of shear stress at the wall is enhanced, suggesting that, if applied to vascular system, the vascular wall could be prone to ulceration during pathological situations like polycythemia. The delay in adaptation of the deviation in Poiseuille flow velocity to the curvature changes is also discussed in detail.

Carrier density-dependent transport in poly(3-methylthiophene): from injection-limited to space-charge-limited current

Current-voltage (I-V) and impedance measurements were carried out in doped poly(3-methylthiophene) devices by varying the carrier density. As the carrier concentration reduces the I-V characteristics indicate that the conduction mechanism is limited by metal-polymer interface, as also observed in impedance data. The temperature dependence of I-V in moderately doped samples shows a trap-controlled space-charge-limited conduction (SCLC); whereas in lightly doped devices injection-limited conduction is observed at lower bias and SCLC at higher voltages. The carrier density-dependent quasi-Fermi level adjustment and trap-limited transport could explain this variation in conduction mechanism. Capacitance measurements at lower frequencies and higher bias voltages show a sign change in values due to the significant variations in the relaxation behaviour for lightly and moderately doped samples. The electrical hysteresis increases as carrier density is reduced due to the time scales involved in the de-trapping of carriers.

Matrix Crack Detection in Composite Plate with Spatially Random Material Properties using Fractal Dimension

Fractal dimension based damage detection method is investigated for a composite plate with random material properties. Composite material shows spatially varying random material properties because of complex manufacturing processes. Matrix cracks are considered as damage in the composite plate. Such cracks are often seen as the initial damage mechanism in composites under fatigue loading and also occur due to low velocity impact. Static deflection of the cantilevered composite plate with uniform loading is calculated using the finite element method. Damage detection is carried out based on sliding window fractal dimension operator using the static deflection. Two dimensional homogeneous Gaussian random field is generated using Karhunen-Loeve (KL) expansion to represent the spatial variation of composite material property. The robustness of fractal dimension based damage detection method is demonstrated considering the composite material properties as a two dimensional random field.

Matrix crack detection in spatially random composite structures using fractal dimension

Fractal dimension based damage detection method is studied for a composite structure with random material properties. A composite plate with localized matrix crack is considered. Matrix cracks are often seen as the initial damage mechanism in composites. Fractal dimension based method is applied to the static deformation curve of the structure to detect localized damage. Static deflection of a cantilevered composite plate under uniform loading is calculated using the finite element method. Composite material shows spatially varying random material properties because of complex manufacturing processes. Spatial variation of material property is represented as a two dimensional homogeneous Gaussian random field. Karhunen-Loeve (KL) expansion is used to generate a random field. The robustness of fractal dimension based damage detection methods is studied considering the composite plate with spatial variation in material properties.

Spatial correlations around a Kondo impurity

We present a method for calculating zero-frequency, spatially varying response and correlation functions around a magnetic impurity in metals. We illustrate the procedure which involves a combination of perturbative scaling and nonperturbative renormalization-group methods for the spin-(1/2) Kondo impurity. We explain the factorization of the temperature and spatial dependence of the Knight shift observed in NMR experiments.

Injection cooling of blunt bodies flying at high Mach numbers

A study of transpiration cooling of blunt bodies such as a hemicylinder is made by solving Navier-Stokes equations. An upwind, implicit time-marching code is developed for this purpose. The study is conducted for both perfect-gas and real-gas (chemical equilibrium) flows. Investigations are carried out for a special wall condition that is referred to as no heat flow into the wall condition. The effects of air injection on wall temperature are analyzed. Analyses are carried out for Mach numbers ranging between 6-10 and Reynolds numbers ranging between 10(6)-10(7). Studies are made for spatially constant as well as spatially varying mass injection rate distributions, White cold air injection reduces the wall temperature substantially, transpiration cooling is relatively less effective when the gas is in chemical equilibrium.

Optimised form of acceleration correction algorithm within SPH-based simulations of impact mechanics

In the context of SPH-based simulations of impact dynamics, an optimised and automated form of the acceleration correction algorithm (Shaw and Reid, 2009a) is developed so as to remove spurious high frequency oscillations in computed responses whilst retaining the stabilizing characteristics of the artificial viscosity in the presence of shocks and layers with sharp gradients. A rational framework for an insightful characterisation of the erstwhile acceleration correction method is first set up. This is followed by the proposal of an optimised version of the method, wherein the strength of the correction term in the momentum balance and energy equations is optimised. For the first time, this leads to an automated procedure to arrive at the artificial viscosity term. In particular, this is achieved by taking a spatially varying response-dependent support size for the kernel function through which the correction term is computed. The optimum value of the support size is deduced by minimising the (spatially localised) total variation of the high oscillation in the acceleration term with respect to its (local) mean. The derivation of the method, its advantages over the heuristic method and issues related to its numerical implementation are discussed in detail. (C) 2011 Elsevier Ltd. All rights reserved.

Dynamic properties of sand from dry to fully saturated states

By using bender and extender elements test, the velocities of the primary and shear waves, V(P) and V(s) respectively, were measured for a sandy material by gradually varying the degree of saturation, S(r), between the dry and fully saturated states. The effect on the results of varying the relative density and effective confining pressure was also studied. The measurements clearly reveal that for a certain optimum S(r), which is around 0.7-0.9% for the chosen sand, the value of the shear modulus G reaches a maximum value, whereas the corresponding Poisson's ratio nu attains a minimum value. The values of the shear modulus corresponding to S(r) approximate to 0% and S(r) = 100% tend towards the same value. For values of Skempton's B parameter greater than 0.99, the values of V(P) and nu rise very sharply to those of water. The predictions from Biot's theory with respect to the variation of V(P) with S(r) match well with the measured experimental data.

Fidelity susceptibility of one-dimensional models with twisted boundary conditions

Recently it has been shown that the fidelity of the ground state of a quantum many-body system can be used todetect its quantum critical points (QCPs). If g denotes the parameter in the Hamiltonian with respect to which the fidelity is computed, we find that for one-dimensional models with large but finite size, the fidelity susceptibility chi(F) can detect a QCP provided that the correlation length exponent satisfies nu < 2. We then show that chi(F) can be used to locate a QCP even if nu >= 2 if we introduce boundary conditions labeled by a twist angle N theta, where N is the system size. If the QCP lies at g = 0, we find that if N is kept constant, chi(F) has a scaling form given by chi(F) similar to theta(-2/nu) f (g/theta(1/nu)) if theta << 2 pi/N. We illustrate this both in a tight-binding model of fermions with a spatially varying chemical potential with amplitude h and period 2q in which nu = q, and in a XY spin-1/2 chain in which nu = 2. Finally we show that when q is very large, the model has two additional QCPs at h = +/- 2 which cannot be detected by studying the energy spectrum but are clearly detected by chi(F). The peak value and width of chi(F) seem to scale as nontrivial powers of q at these QCPs. We argue that these QCPs mark a transition between extended and localized states at the Fermi energy. DOI: 10.1103/PhysRevB.86.245424

Improved modeling of groundwater recharge in agricultural watersheds using a combination of crop model and remote sensing

For improved water management and efficiency of use in agriculture, studies dealing with coupled crop-surface water-groundwater models are needed. Such integrated models of crop and hydrology can provide accurate quantification of spatio-temporal variations of water balance parameters such as soil moisture store, evapotranspiration and recharge in a catchment. Performance of a coupled crop-hydrology model would depend on the availability of a calibrated crop model for various irrigated/rainfed crops and also on an accurate knowledge of soil hydraulic parameters in the catchment at relevant scale. Moreover, such a coupled model should be designed so as to enable the use/assimilation of recent satellite remote sensing products (optical and microwave) in order to model the processes at catchment scales. In this study we present a framework to couple a crop model with a groundwater model for applications to irrigated groundwater agricultural systems. We discuss the calibration of the STICS crop model and present a methodology to estimate the soil hydraulic parameters by inversion of crop model using both ground and satellite based data. Using this methodology we demonstrate the feasibility of estimation of potential recharge due to spatially varying soil/crop matrix.

Dynamic state estimation for identifying earthquake support motions in instrumented structures

The problem of identification of multi-component and (or) spatially varying earthquake support motions based on measured responses in instrumented structures is considered. The governing equations of motion are cast in the state space form and a time domain solution to the input identification problem is developed based on the Kalman and particle filtering methods. The method allows for noise in measured responses, imperfections in mathematical model for the structure, and possible nonlinear behavior of the structure. The unknown support motions are treated as hypothetical additional system states and a prior model for these motions are taken to be given in terms of white noise processes. For linear systems, the solution is developed within the Kalman filtering framework while, for nonlinear systems, the Monte Carlo simulation based particle filtering tools are employed. In the latter case, the question of controlling sampling variance based on the idea of Rao-Blackwellization is also explored. Illustrative examples include identification of multi-component and spatially varying support motions in linear/nonlinear structures.

Improving tangential resolution with a modified delay-and-sum reconstruction algorithm in photoacoustic and thermoacoustic tomography

Spatial resolution in photoacoustic and thermoacoustic tomography is ultrasound transducer (detector) bandwidth limited. For a circular scanning geometry the axial (radial) resolution is not affected by the detector aperture, but the tangential (lateral) resolution is highly dependent on the aperture size, and it is also spatially varying (depending on the location relative to the scanning center). Several approaches have been reported to counter this problem by physically attaching a negative acoustic lens in front of the nonfocused transducer or by using virtual point detectors. Here, we have implemented a modified delay-and-sum reconstruction method, which takes into account the large aperture of the detector, leading to more than fivefold improvement in the tangential resolution in photoacoustic (and thermoacoustic) tomography. Three different types of numerical phantoms were used to validate our reconstruction method. It is also shown that we were able to preserve the shape of the reconstructed objects with the modified algorithm. (C) 2014 Optical Society of America

Gammatone Wavelet Cepstral Coefficients for Robust Speech Recognition

We develop noise robust features using Gammatone wavelets derived from the popular Gammatone functions. These wavelets incorporate the characteristics of human peripheral auditory systems, in particular the spatially-varying frequency response of the basilar membrane. We refer to the new features as Gammatone Wavelet Cepstral Coefficients (GWCC). The procedure involved in extracting GWCC from a speech signal is similar to that of the conventional Mel-Frequency Cepstral Coefficients (MFCC) technique, with the difference being in the type of filterbank used. We replace the conventional mel filterbank in MFCC with a Gammatone wavelet filterbank, which we construct using Gammatone wavelets. We also explore the effect of Gammatone filterbank based features (Gammatone Cepstral Coefficients (GCC)) for robust speech recognition. On AURORA 2 database, a comparison of GWCCs and GCCs with MFCCs shows that Gammatone based features yield a better recognition performance at low SNRs.