Backward Components Research Articles

Simple unidirectional finite-energy pulses

We obtain a family of simple closed-form exact solutions of the three-dimensional wave equation that are free of backward components. The solutions have no singularities and possess finite energy. They describe single-cycle and subcycle pulses. Depending on two parameters, the family yields pulses with different types of localization, in particular, focused pancakes, balls, and needles.

Double-sampled differential square-wave voltammetry

A differential form of square-wave voltammetry (SWV) is proposed based on a double sampling current protocol within the last quarter of the duration of each potential pulse. Differential forward (Id,f) and backward (Id,b) current components are well defined peaks with precisely accessible peak characteristics, which is not the case in conventional variant of the technique where most frequently one encounters asymmetric or sigmoid curves. The proposed methodology is theoretically tested with a simple quasi-reversible electrode reaction of a dissolved redox couple at a macroscopic planar electrode, as well as with the mechanism where the electrode reaction is coupled with a follow-up chemical reaction (i.e. ECr mechanism). Besides expected advances in analytical context, the proposed methodology is promising for mechanistic and kinetic analysis by inspecting the features of the forward and backward current components for any degree of electrochemical reversibility. Thus, the common analysis of the net peak current in conventional SWV can be replaced with the peak current ratio of the forward-to-backward (Ip,f/Ip,b) current components in the differential variant of the technique. The peak current ratio is a dimensionless, relative parameter enabling a straightforward comparison to experimental data, which is not always the case with the net peak current of the conventional SWV.

Measurement, Analysis and Interpretation of Pressure/Flow Waves in Blood Vessels.

The optimal performance of the cardiovascular system, as well as the break-down of this performance with disease, both involve complex biomechanical interactions between the heart, conduit vascular networks and microvascular beds. ‘Wave analysis’ refers to a group of techniques that provide valuable insight into these interactions by scrutinizing the shape of blood pressure and flow/velocity waveforms. The aim of this review paper is to provide a comprehensive introduction to wave analysis, with a focus on key concepts and practical application rather than mathematical derivations. We begin with an overview of invasive and non-invasive measurement techniques that can be used to obtain the signals required for wave analysis. We then review the most widely used wave analysis techniques—pulse wave analysis, wave separation and wave intensity analysis—and associated methods for estimating local wave speed or characteristic impedance that are required for decomposing waveforms into forward and backward wave components. This is followed by a discussion of the biomechanical phenomena that generate waves and the processes that modulate wave amplitude, both of which are critical for interpreting measured wave patterns. Finally, we provide a brief update on several emerging techniques/concepts in the wave analysis field, namely wave potential and the reservoir-excess pressure approach.

Usefulness of Proximal Coronary Wave Speed for Wave Intensity Analysis in Diseased Coronary Vessels.

Background: Wave speed is needed to separate net wave intensity into forward and backward traveling components. However, wave speed in diseased coronary arteries cannot be assessed from hemodynamic measurements obtained distal to a stenosis. Wave speed inherently depends on arterial wall properties which should be similar proximal and distal to a stenosis. Our hypothesis is that proximal wave speed can be used to separate net wave intensity obtained distal to a stenosis.Methods: We assessed coronary wave speed using the sum-of-squares single-point technique (SPc) based on simultaneous intracoronary pressure and flow velocity measurements in human coronary arteries. SPc at resting flow was determined in diseased coronary vessels of 12 patients both proximal and distal to the stenosis. In seven of these vessels, distal measurements were additionally obtained after revascularization by stent placement. SPc was also assessed at two axial locations in 14 reference vessels without a stenosis.Results: (1) No difference in SPc was present between proximal and distal locations in the reference vessels. (2) In diseased vessels with a focal stenosis, SPc at the distal location was paradoxically larger than SPc proximal to the stenosis (28.4 ± 3.7 m/s vs. 18.3 ± 1.8 m/s, p < 0.02), despite the lower distending pressure downstream of the stenosis. The corresponding separated wave energy tended to be underestimated when derived from SPc at the distal compared with the proximal location. (3) After successful revascularization, SPc at the distal location no longer differed from SPc at the proximal location prior to revascularization (21.9 ± 2.0 m/s vs. 20.8 ± 1.9 m/s, p = 0.48). Accordingly, no significant difference in separated wave energy was observed for forward or backward waves.Conclusion: In diseased coronary vessels, SPc assessed from distal hemodynamic signals is erroneously elevated. Our findings suggest that proximal wave speed can be used to separate wave intensity profiles obtained downstream of a stenosis. This approach may extend the application of wave intensity analysis to diseased coronary vessels.

Simulating re-reflections of arterial pressure waves at the aortic valve using difference equations

Re-reflections of arterial pressure waves at the aortic valve and their influence on aortic wave shape are only poorly understood so far. Therefore, the aim of this work is to establish a model enabling the simulation of re-reflection and to test its properties. A mathematical difference equation model is used for the simulations. In this model, the aortic blood pressure is split into its forward and backward components which are calculated separately. The respective equations include reflection percentages representing reflections throughout the arterial system and a reflection coefficient at the aortic valve. While the distal reflections are fixed, different scenarios for the reflection coefficient at the valve are simulated. The results show that the model is capable to provide physiological pressure curves only if re-reflections are assumed to be present during the whole cardiac cycle. The sensitivity analysis on the reflection coefficient at the aortic valve shows various effects of re-reflections on the modelled blood pressure curve. Higher levels of the reflection coefficient lead to higher systolic and diastolic pressure values. The augmentation index is notably influenced by the systolic level of the reflection coefficient. This difference equation model gives an adequate possibility to simulate aortic pressure incorporating re-reflections at the site of the aortic valve. Since a strong dependence of the aortic pressure wave on the choice of the reflection coefficient have been found, this indicates that re-reflections should be incorporated into models of wave transmission. Furthermore, re-reflections may also be considered in methods of arterial pulse wave analysis.

Electromagnetic Duality Protected Scattering Properties of Nonmagnetic Particles

Optical properties of nonmagnetic structures that support artificial optically-induced magnetic responses have recently attracted surging interest. Here we conduct symmetry-dictated investigations into scattering properties of nonmagnetic particles from perspectives of electromagnetic duality with discrete geometric rotations. For arbitrary scattering configurations, we reveal that far-field scattering patterns are invariant under duality transformations, which in particular means that scattering patterns of self-dual clusters with random particle distributions are polarization independent. Based on this revelation, it is further discovered that scattering bodies of combined duality-(n-fold) rotation symmetry, for any polarizations of incident waves, exhibit also n-fold rotationally symmetric scattering patterns with zero backward components, satisfying the first Kerker condition automatically. We employ both coupled dipole theory and full numerical simulations to demonstrate those scattering properties, solely based upon nonmagnetic core-shell particles that support optically-induced dipolar resonances. Those substantiated scattering properties are fully induced by fundamental symmetry principles, and thus can survive any non-symmetry-breaking perturbations, which may find applications in a wide range of optical devices that require intrinsically robust functionalities.

Electrode mechanisms with coupled chemical reaction — Amplitude effect in square-wave voltammetry

This article presents the theoretical prediction of square-wave amplitude effect on electrode reaction mechanisms coupled with chemical reaction under conditions of square-wave voltammetry. A systematic change in simulated voltammograms occurs following a change in the applied square-wave amplitude parameter. The obtained results help to assess the generated impact on the peak potential separation of square-wave forward and backward components from conventional and potential corrected voltammograms as well as on the so-called ‘amplitude-based quasireversible maximum’ acquired during the analysis of the net response peak height. In most cases, these features are independent of the parameters of coupled chemical reaction, and electrode kinetics can be estimated without their prior knowledge. Some characteristic criteria can be deduced from the observed trends, which can serve as a means to elucidate electron transfer kinetics. Under these conditions, even nonexperts in the square-wave voltammetry technique can characterize the studied experimental systems.

Single-ended fault location for direct distribution overhead feeders based on characteristic distribution of traveling waves along the line

To decrease the location error brought by reflected wave crest identification for direct distribution overhead feeders in non-effective grounding system based on single-ended traveling location method, a novel location method is proposed in this paper. Taking advantage of transient information measured at line terminals, Bergeron Transfer Equation is utilized for calculation of voltage and current traveling waves along the faulty feeder. A location function is then built by the forward and backward traveling-wave components to describe the energy distribution of traveling-wave catastrophe. The method is of high precision and feasible for direct distribution overhead feeders through PSCAD simulation. Various measurement conditions are also taken into consideration.

Single-Ended Fault Location for Hybrid Feeders Based on Characteristic Distribution of Traveling Wave Along a Line

In terms of single-ended fault location for hybrid distribution lines, the most significant challenge is in the identification of the fault section and reflected wave from the fault point. Based on this, in this paper we introduce a new fault- section-location identification scheme for hybrid distribution feeders with only single-ended measurement. With the prior morphological spectrum-based fault-section identification technique, a location function is then built by the forward and backward traveling-wave components to describe the characteristic distribution of the traveling wave along the line. With the application of two-dimensional information (which is about time and space) of the traveling wave, it is simpler to locate the actual point of failure. The proposed scheme is investigated under different fault locations, fault resistances, sampling rates, fault inception angles, fault types, etc. The influences of immeasurable voltage traveling wave, adjacent sound lines, and measurable joint point are also investigated. Simulation results confirm the feasibility of the fault-location scheme for all test cases.

Two phase motor fed from controlled supply

&lt;p&gt;Compared to single phase operation, a good utilization of machine material is achieved by supplying the two-phase stator windings from a controlled supply. It is necessary to start from the known equivalent circuits of both forward and backward components to obtain the relations between the sequence and the phase voltage values. In this method of control, the torque expression is driven in a simple form and the torque speed characteristic are computed and plotted for different values of the time-phase angle. The operation of 2-phase motor from single phase supply carried out by connecting one stator phase directly to the voltages source, with exciting the second stator phase through the phase shifting element. In this method, the starting and the maximum torque values can be controlled by changing the stator field from a pulsating of (0°) to a pure rotating field at (90°).&lt;/p&gt;

Necessary condition for optimal control of doubly stochastic systems

The aim of this paper is to establish a necessary condition for optimal stochastic controls where the systems governed by forward-backward doubly stochastic differential equations (FBDSDEs in short). The control constraints need not to be convex. This condition is described by two kinds of new adjoint processes containing two Brownian motions, corresponding to the forward and backward components and a maximum condition on the Hamiltonian. The proof of the main result is based on spike's variational principle, duality technique and delicate estimates on the state and the adjoint processes with respect to the control variable. An example is provided for illustration.

Differential Square-Wave Voltammetry.

A new voltammetric technique designed as a hybrid between differential pulse and square-wave voltammetry is proposed for the purpose of unifying the advantages of both techniques, i.e., the ability to provide mechanistic information, studying electrode kinetics of both sluggish and very fast electrode reactions, and the ability to suppress effectively residual background current. Voltammetric modulation of the hybrid technique consists of a staircase potential combined with square-wave potential modulation superimposed at the end of each potential step. By measuring the current at the end of each potential step and pulse, differential forward and backward voltammetric components can be composed, which is a unique ability of the hybrid technique. In addition, by analogy to square-wave voltammetry, a net differential component can be contracted with improved analytical performances compared to square-wave voltammetry. The proposed technique opens a new avenue for an advanced analysis of electrochemical processes and analytical application.

Step potential as a diagnostic tool in square-wave voltammetry of quasi-reversible electrochemical processes

By applying square-wave voltammetry (SWV) and through examining the most common electrochemical kinetic region, i.e. the quasi-reversible charge transfer process, the important role of the step potential (height, ΔE) was theoretically and practically studied considering both, the dissolved as well as the electrode surface confined redox species. It was found that the impact of the step potential is readily manifested through the scan rate (v) of an SWV experiment, the one being the product of the frequency of pulses (f) and the step potential (v = ΔE f). The presented studies evidently confirmed that the role of the step potential is very complex but that it significantly affects the morphology of both, the forward as well as the backward SWV current components, which applies for any degree of electrochemical reversibility. Furthermore, it was demonstrated that in case of quasi-reversible electrochemical reactions the degree of reversibility profoundly depends on the step potential applied. Moreover, it was proven that the degree of reversibility can be markedly improved by correspondingly decreasing ΔE. This has significant importance in the context of electrode kinetics as well as in analytical applications. Hence, this study clearly demonstrated that besides the frequency, the step potential can be an additional important tool for inspecting and improving the electrode kinetics in SWV. Finally, in order to test a practical example of a quasireversible electrode reaction of a dissolved redox couple, the SWV measurements of theFe3+(aq)/Fe2+(aq) redox couple were carried out using a basal plane pyrolytic graphite electrode and the resulting readings confirmed our theoretical predictions.

Two Phase Motor under Control

The use of symmetrical two-phase stator windings with time phase control, (leaving the phase voltages eqal in magnitudes), leads to better utilization of machine material. This aidea can be extended to include many methods of control such as amplitude control, time-phase control, frequency control, voltage control and voltage-frequency control methods. If any of these methods is used, either Vc, , f and/or Vr may be varied with the control signal. For these sugested methods, the reference voltage Vr, changes w.r.t nominal voltage Vrn, the frequency changes w.r.t the nominal frequency fn, the control voltage Vc, changes w.r.t nominal voltage Vrn and the time phase angle  decreases than 90o, respectively. In this paper, the operation of 2-phase motor from single-phase supply is carried out by connecting one stator phase directly to the voltage source, and exciting the second stator phase through a phase shifting element.Compared to single-phase operation, good performance characteristics with higher starting torque are achieved. It is necessary to start the analysis by using the known equivalent circuits of both forward and backward components to obtain the relations between the sequence parameters and the phase values. In this method of control, starting torque and maximum torque values are controlled by changing the stator field from a pulsating field at zero degree to a pure rotating field which must be achieved at 90o electrical degrees.

Optimal execution with dynamic risk adjustment

This article considers the problem of optimal liquidation of a position in a risky security quoted in a financial market, where price evolution are risky and trades have an impact on price as well as uncertainty in the filling orders. The problem is formulated as a continuous time stochastic optimal control problem aiming at maximising a generalised risk-adjusted profit and loss function. The expression of the risk adjustment is derived from the general theory of dynamic risk measures and is selected in the class of g-conditional risk measures. The resulting theoretical framework is nonclassical since the target function depends on backward components. We show that, under a quadratic specification of the driver of a backward stochastic differential equation, it is possible to find a closed form solution and an explicit expression of the optimal liquidation policies. In this way, it is immediate to quantify the impact of risk adjustment on the profit and loss and on the expression of the optimal liquidation policies.

A Mild-Slope System for Bragg Scattering of Water Waves by Sinusoidal Bathymetry in the Presence of Vertically Sheared Currents

Extended mild-slope models (MMSs) are examined for predicting the characteristics of normally incident waves propagating over sinusoidal bottom topography in the presence of opposing shearing currents. It is shown that MMSs are able to provide quite good predictions in the case of Bragg scattering of waves over rippled bathymetry without a current, but fail to provide good predictions concerning the resonant frequency in the additional presence of a current. In order to resolve the above mismatch, a two-equation mild-slope system (CMS2) is derived from a variational principle based on the representation of the wave potential expressed as a superposition of the forward and backward components. The latter system is compared against experimentally measured data collected in a wave flume and is shown to provide more accurate predictions concerning both the resonant frequency and the amplitude of the reflection coefficient. Future work will be devoted to the examination of the derived model for a more general wave system over realistic seabed topography.

Polariton Propagation in Imperfect Resonantly Absorbing Bragg grating

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Reliability of pulse waveform separation analysis responses to an orthostatic challenge.

Cardiovascular autonomic nervous system function can be assessed using an orthostatic challenge to induce arterial wave reflection. While arterial reflection is typically estimated using a central augmentation index, a superior estimation can be obtained using pulse wave separation analysis to estimate the aortic backward pressure wave (Pb). However, to be of value in a clinical or research setting, an assessment tool must be precise (reliable). Therefore, this study sought to determine the measurement precision of Pb responses to a modified tilt-table test. Twenty healthy adults (26.4 year (SD 5.2), 24.7 kg/m2 (SD 3.8), 55% female) were tested in a fasted state on three different mornings separated by a maximum of seven days. Pressure waveforms were recorded on the left arm, and aortic waveforms were generated using a generalized transfer function. Subsequently, a physiologic flow waveform was assumed to separate the aortic pressure wave into its forward and timing-independent backward (Pb) components. The criterion intra-class correlation coefficient of ≥0.75 was exceeded at baseline (0.79), following a 5-min tilt (0.75), and following a 5-min recovery from tilt (0.75). The standard error of measurement was 7%. These findings indicate that in a healthy cohort, the Pb response to an orthostatic challenge can be assessed with acceptable precision. The next step is to determine the sensitivity (validity) of this technique in identifying cardiovascular autonomic dysfunction in patient groups.

Solution to Discrete-Time Linear FBSDEs with Application to Stochastic Control Problem

In this paper, we consider a class of infinite horizon forward and backward stochastic difference equations (FBSDEs) that are fully coupled. The adapted solution is given by establishing an explicit relation between the forward and backward components in terms of a generalized algebraic Riccati equation. The equivalence between the exponential stabilizability of the stochastic control system and the infinite horizon FBSDEs is derived. As an application, the FBSDEs are used to characterize the maximum principle of the infinite horizon stochastic optimal control problem.

Evolution of aortic pressure during normal ageing: A model-based study.

BackgroundThe age-related increase in pulse pressure (PP) and systolic blood pressure (SBP) is often attributed to alterations in the wave reflection profile and augmented contributions of the reflected waves. However, clinical evidence shows that the stiffening of the proximal aorta with age and the consequent augmentation of the forward pressure wave plays an equally important role. The relative importance of the forward and reflected wave components in essential hypertension has not yet been fully elucidated.ObjectiveThe aim of the current investigation was to simulate the major ageing mechanisms in the arterial system and the heart using a mathematical one-dimensional model of the arterial tree and to assess the evolution of systolic and pulse pressure during normal (non-pathological) ageing.Methods and resultsOur state-of-the-art 1-D model was extended to include turbulence and inertial effects of the flow exiting the left ventricle. Literature data on the age-associated changes in arterial stiffness, peripheral resistance and cardiac contractility were gathered and used as an input for the simulations. The predicted evolution of pressure and augmentation index with age followed accurately the curves obtained in a number of large-scale clinical studies. Analysis of the relative contribution of the forward and backward wave components showed that the forward wave becomes the major determinant of the increase in central and peripheral SBP and PP with advancing age.ConclusionsThe 1-D model of the ageing tree and heart captures faithfully and with great accuracy the central pressure evolution with ageing. The stiffening of the proximal aorta and the resulting augmentation of the forward pressure wave is the major contributor of the systolic pressure augmentation with age.