A hybrid Laplace transform/finite difference boundary element method for diffusion problems

The solution process for diffusion problems usually involves the time development separately from the space solution. A finite difference algorithm in time requires a sequential time development in which all previous values must be determined prior to the current value. The Stehfest Laplace transform algorithm, however, allows time solutions without the knowledge of prior values. It is of interest to be able to develop a time-domain decomposition suitable for implementation in a parallel environment. One such possibility is to use the Laplace transform to develop coarse-grained solutions which act as the initial values for a set of fine-grained solutions. The independence of the Laplace transform solutions means that we do indeed have a time-domain decomposition process. Any suitable time solver can be used for the fine-grained solution. To illustrate the technique we shall use an Euler solver in time together with the dual reciprocity boundary element method for the space solution

A time-domain approach to the analysis and modeling of on-body propagation characteristics using synchronized measurements at 2.45 GHz

Modeling of on-body propagation channels is of paramount importance to those wishing to evaluate radio channel performance for wearable devices in body area networks (BANs). Difficulties in modeling arise due to the highly variable channel conditions related to changes in the user's state and local environment. This study characterizes these influences by using time-series analysis to examine and model signal characteristics for on-body radio channels in user stationary and mobile scenarios in four different locations: anechoic chamber, open office area, hallway, and outdoor environment. Autocorrelation and cross-correlation functions are reported and shown to be dependent on body state and surroundings. Autoregressive (AR) transfer functions are used to perform time-series analysis and develop models for fading in various on-body links. Due to the non-Gaussian nature of the logarithmically transformed observed signal envelope in the majority of mobile user states, a simple method for reproducing the failing based on lognormal and Nakagami statistics is proposed. The validity of the AR models is evaluated using hypothesis testing, which is based on the Ljung-Box statistic, and the estimated distributional parameters of the simulator output compared with those from experimental results.

Combined R-matrix eigenstate basis set and finite-difference propagation method for the time-dependent Schrodinger equation: The one-electron case

In this work we present the theoretical framework for the solution of the time-dependent Schrödinger equation (TDSE) of atomic and molecular systems under strong electromagnetic fields with the configuration space of the electron’s coordinates separated over two regions; that is, regions I and II. In region I the solution of the TDSE is obtained by an R-matrix basis set representation of the time-dependent wave function. In region II a grid representation of the wave function is considered and propagation in space and time is obtained through the finite-difference method. With this, a combination of basis set and grid methods is put forward for tackling multiregion time-dependent problems. In both regions, a high-order explicit scheme is employed for the time propagation. While, in a purely hydrogenic system no approximation is involved due to this separation, in multielectron systems the validity and the usefulness of the present method relies on the basic assumption of R-matrix theory, namely, that beyond a certain distance (encompassing region I) a single ejected electron is distinguishable from the other electrons of the multielectron system and evolves there (region II) effectively as a one-electron system. The method is developed in detail for single active electron systems and applied to the exemplar case of the hydrogen atom in an intense laser field.

Patellofemoral pain syndrome: Electromyography in a frequency domain analysis

The Patellofemoral Pain Syndrome (PFPS), has a multifactorial etiology and affects approximately 7 to 15% of the population, mostly women, youth, adults and active persons. PFPS causes anterior or retropatelar pain that is exacerbated during functional motor gestures, such as up and down stairs or spending long periods of time sitting, squatting or kneeling. As the diagnostic evaluation of this syndrome is still indirect, different mechanisms and methodologies try to make a classification that distinguishes patients with PFPS in relation to asymptomatic. Thereby, the purpose of this investigation was to determine the characteristics of the electromyographic (EMG) signal in the frequency domain of the vastus medialis oblique (VMO) and vastus lateralis (VL) in patients with PFPS, during the ascent of stairs. 33 young women (22 control group and 11 PFPS group), were evaluated by EMG during ascent of stairs. The VMO mean power frequency (MPF) and the VL frequency 95% (F95) were lower in symptomatic individuals. This may be related to the difference in muscle recruitment strategy exerted by each muscle in the PFPS group compared to the control group.

A Time-domain Harmonic Power-Flow Analysis in Electrical Energy Distribution Networks, Using Norton Models for Non-linear Loading

The purpose of this paper is to present the application of a three-phase harmonic propagation analysis time-domain tool, using the Norton model to approach the modeling of non-linear loads, making the harmonics currents flow more appropriate to the operation analysis and to the influence of mitigation elements analysis. This software makes it possible to obtain results closer to the real distribution network, considering voltages unbalances, currents imbalances and the application of mitigation elements for harmonic distortions. In this scenario, a real case study with network data and equipments connected to the network will be presented, as well as the modeling of non-linear loads based on real data obtained from some PCCs (Points of Common Coupling) of interests for a distribution company.

Comparison between frequency domain and time domain riser analysis

In the optimization or parametric analyses of risers, several configurations must be analyzed. It is laborious to perform time domain solutions for the dynamic analysis, since they are time-consuming tasks. So, frequency domain solutions appear to be a possible alternative, mainly in the early stages of a riser design. However, frequency domain analysis is linear and requires that nonlinear effects are treated. The aim of this paper is to present a possible way to treat some of these nonlinearities, using an iterative process together with an analytical correction, and compare the results of a frequency domain analysis with the those of a full nonlinear analysis. [DOI: 10.1115/1.4006149]

Ethanol fuel analysis by time-domain reflectometry

The technique of Time Domain Reflectometry (TDR) is applied for qualifying ethanol adulterated with water and / or methanol. We used the commercial TDR model VG400, which was originally developed for determining soil moisture, making this study an original approach for qualifying fuels. Several samples of alcohol with the addition of its main contaminants (water and methanol) were prepared and measured with the TDR sensor. The results indicate good response linearity, showing the TDR technique is a promising technique for fuel qualification

Finite difference calculations of permeability in large domains in a wide porosity range.

Determining effective hydraulic, thermal, mechanical and electrical properties of porous materials by means of classical physical experiments is often time-consuming and expensive. Thus, accurate numerical calculations of material properties are of increasing interest in geophysical, manufacturing, bio-mechanical and environmental applications, among other fields. Characteristic material properties (e.g. intrinsic permeability, thermal conductivity and elastic moduli) depend on morphological details on the porescale such as shape and size of pores and pore throats or cracks. To obtain reliable predictions of these properties it is necessary to perform numerical analyses of sufficiently large unit cells. Such representative volume elements require optimized numerical simulation techniques. Current state-of-the-art simulation tools to calculate effective permeabilities of porous materials are based on various methods, e.g. lattice Boltzmann, finite volumes or explicit jump Stokes methods. All approaches still have limitations in the maximum size of the simulation domain. In response to these deficits of the well-established methods we propose an efficient and reliable numerical method which allows to calculate intrinsic permeabilities directly from voxel-based data obtained from 3D imaging techniques like X-ray microtomography. We present a modelling framework based on a parallel finite differences solver, allowing the calculation of large domains with relative low computing requirements (i.e. desktop computers). The presented method is validated in a diverse selection of materials, obtaining accurate results for a large range of porosities, wider than the ranges previously reported. Ongoing work includes the estimation of other effective properties of porous media.

Effects of increasing neuromuscular electrical stimulation current intensity on cortical sensorimotor network activation: A time domain fNIRS study

Neuroimaging studies have shown neuromuscular electrical stimulation (NMES)-evoked movements activate regions of the cortical sensorimotor network, including the primary sensorimotor cortex (SMC), premotor cortex (PMC), supplementary motor area (SMA), and secondary somatosensory area (S2), as well as regions of the prefrontal cortex (PFC) known to be involved in pain processing. The aim of this study, on nine healthy subjects, was to compare the cortical network activation profile and pain ratings during NMES of the right forearm wrist extensor muscles at increasing current intensities up to and slightly over the individual maximal tolerated intensity (MTI), and with reference to voluntary (VOL) wrist extension movements. By exploiting the capability of the multi-channel time domain functional near-infrared spectroscopy technique to relate depth information to the photon time-of-flight, the cortical and superficial oxygenated (O₂Hb) and deoxygenated (HHb) hemoglobin concentrations were estimated. The O₂Hb and HHb maps obtained using the General Linear Model (NIRS-SPM) analysis method, showed that the VOL and NMES-evoked movements significantly increased activation (i.e., increase in O₂Hb and corresponding decrease in HHb) in the cortical layer of the contralateral sensorimotor network (SMC, PMC/SMA, and S2). However, the level and area of contralateral sensorimotor network (including PFC) activation was significantly greater for NMES than VOL. Furthermore, there was greater bilateral sensorimotor network activation with the high NMES current intensities which corresponded with increased pain ratings. In conclusion, our findings suggest that greater bilateral sensorimotor network activation profile with high NMES current intensities could be in part attributable to increased attentional/pain processing and to increased bilateral sensorimotor integration in these cortical regions.

Numerical study of heat transfer in laminar film boiling by the finite-difference method

The finite-difference form of the basic conservation equations in laminar film boiling have been solved by the false-transient method. By a judicious choice of the coordinate system the vapour-liquid interface is fitted to the grid system. Central differencing is used for diffusion terms, upwind differencing for convection terms, and explicit differencing for transient terms. Since an explicit method is used the time step used in the false-transient method is constrained by numerical instability. In the present problem the limits on the time step are imposed by conditions in the vapour region. On the other hand the rate of convergence of finite-difference equations is dependent on the conditions in the liquid region. The rate of convergence was accelerated by using the over-relaxation technique in the liquid region. The results obtained compare well with previous work and experimental data available in the literature.

Time Domain Characteristics of Electrical Measures for a Piezoelectric Thin Film to Identify Defects in the Substrate

A reduced 3D continuum model of dynamic piezoelectricity in a thin-film surface-bonded to the substrate/host is presented in this article. While employing large area flexible thin piezoelectric films for novel applications in device/diagnostics, the feasibility of the proposed model in sensing the surface and/or sub-surface defects is demonstrated through simulations - which involve metallic beams with cracks and composite beam with delaminations of various sizes. We have introduced a set of electrical measures to capture the severity of the damage in the existing structures. Characteristics of these electrical measures in terms of the potential difference and its spatial gradients are illustrated in the time domain. Sensitivity studies of the proposed measures in terms of the defected areas and their region of occurence relative to the sensing film are reported. The simulations' results for electrical measures for damaged hosts/substrates are compared with those due to undamaged hosts/substrates, which show monotonicity with high degree of sensitivity to variations in the damage parameters.

Composite scheme using localized relaxation with non-standard finite difference method for hyperbolic conservation laws

Non-standard finite difference methods (NSFDM) introduced by Mickens [Non-standard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994] are interesting alternatives to the traditional finite difference and finite volume methods. When applied to linear hyperbolic conservation laws, these methods reproduce exact solutions. In this paper, the NSFDM is first extended to hyperbolic systems of conservation laws, by a novel utilization of the decoupled equations using characteristic variables. In the second part of this paper, the NSFDM is studied for its efficacy in application to nonlinear scalar hyperbolic conservation laws. The original NSFDMs introduced by Mickens (1994) were not in conservation form, which is an important feature in capturing discontinuities at the right locations. Mickens [Construction and analysis of a non-standard finite difference scheme for the Burgers–Fisher equations, Journal of Sound and Vibration 257 (4) (2002) 791–797] recently introduced a NSFDM in conservative form. This method captures the shock waves exactly, without any numerical dissipation. In this paper, this algorithm is tested for the case of expansion waves with sonic points and is found to generate unphysical expansion shocks. As a remedy to this defect, we use the strategy of composite schemes [R. Liska, B. Wendroff, Composite schemes for conservation laws, SIAM Journal of Numerical Analysis 35 (6) (1998) 2250–2271] in which the accurate NSFDM is used as the basic scheme and localized relaxation NSFDM is used as the supporting scheme which acts like a filter. Relaxation schemes introduced by Jin and Xin [The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications in Pure and Applied Mathematics 48 (1995) 235–276] are based on relaxation systems which replace the nonlinear hyperbolic conservation laws by a semi-linear system with a stiff relaxation term. The relaxation parameter (λ) is chosen locally on the three point stencil of grid which makes the proposed method more efficient. This composite scheme overcomes the problem of unphysical expansion shocks and captures the shock waves with an accuracy better than the upwind relaxation scheme, as demonstrated by the test cases, together with comparisons with popular numerical methods like Roe scheme and ENO schemes.