Classical numerical methods for solving ordinary differential equations often produce less accurate results when applied to problems with oscillatory or periodic behaviour. To adapt them for such problems, they are usually modified using the exponential fitting technique. This adaptation allows for the construction of new methods from their classical counterparts. The new methods are usually more accurate, efficient and suitable for handling the oscillatory or periodic behaviour of the problem. In this work, we construct a two-parameter exponentially-fitted Taylor method suitable for solving oscillatory or periodic problems that possess two frequencies. The construction algorithm is based on a proposed six-step flowchart discussed by authors in related literature. Two standard test problems were used to illustrate the accuracy and performance of the proposed method.

Two beneficial characteristics of aircraft generators are having armature windings and PM excitation sources placed on the stator side (maintenance and thermal management) and having a clear-cut rotor without permanent magnets or excitation windings (vulnerable at high speeds due to associated centripetal mechanical stresses). Within this framework, a doubly-salient permanent magnet (DSPM) generator was conceived by optimizing the stator size and rotor structure to minimize the torque ripple and maximize the RMS voltage value per turn of each generator phase. A Multi-Objective Design Strategy based on a 2D finite element analysis was used, being set to have characteristics closest to optimal for a Boeing 767 turbine, that is, the necessary electromotive force for a required power of 90 kW at 3000 rpm, feeding a simplified Boeing 767 electrical power distribution system. The results show that the machine could not deliver the required power at 3000 rpm since the 2D finite elements analysis demonstrates that the 2D model gives optimistic results when compared with the 3D FEM model. However, with a 3D finite element analysis of the machine feeding the aircraft load, it was seen that the machine’s efficiency is 92%, suggesting this machine can be a plausible solution.

The quest for accurate and more efficient methods for solving periodic/oscillatory problems is gaining more attention in recent time. This paper presents the construction and implementation of a family of exponentially–fitted Obrechkoff methods. A single–step Obrechkoff method involving terms up to the fourth derivatives was used as the base method. We also present the stability and convergence properties of the constructed family of methods. Two numerical examples were use to illustrate the performance of the constructed methods.

This paper proposed a damping method for enhancing oscillatory stability performance of power systems with high penetration of renewable energy by a resilient wide-area multi-mode controller. The resilient wide-area multi-mode controller is used as an additional controller in a renewable energy system with a battery energy storage to enhance the damping of the critically weak modes. The weak modes are likely to be triggered in the event of line outages or any other disturbances, and the system may become unstable in the absence of proper corrective and preventive control. A firefly algorithm has been employed to design such a controller. Eigenvalue analysis and time-domain simulation are used to analyze the performance of the proposed controller in a realistic representative power system. From the simulation results, it is evident that the oscillatory stability performance of the renewable rich power system can be enhanced with the proposed control to keep the damping on critical modes to the industrial standards. Furthermore, renewable energy penetration can be increased significantly in the realistic representative system by introducing the proposed controller without disturbing the oscillatory stability margin.

To determine the photon emission or absorption probability for a diatomic system in the context of the semiclassical approximation it is necessary to calculate the characteristic canonical oscillatory integral which has one or more saddle points. Integrals like that appear in a whole range of physical problems, e.g. the atom-atom and atom-surface scattering and various optical phenomena. A uniform approximation of the integral, based on the stationary phase method is proposed, where the integral with several saddle points is replaced by a sum of integrals each having only one or at most two real saddle points and is easily soluble. In this way we formally reduce the codimension in canonical integrals of "elementary catastrophes" with codimensions greater than 1. The validity of the proposed method was tested on examples of integrals with three saddle points ("cusp" catastrophe) and four saddle points ("swallow-tail" catastrophe).

By planting LEDs on the surfaces of orifice baffles, a novel batch oscillatory baffled photoreactor (OBPR) together with polymer-supported Rose Bengal (Ps-RB) beads are used to investigate reaction kinetics of a photo-oxidation reaction between α-terpinene and singlet oxygen (1O2). In the widely used NMR data analysis for this reaction, α-terpinene and ascaridole are treated as a reaction pair, assuming kinetically singlet oxygen is in excess or constant. We have, for the first time, examined the validity of the method, discovered that increasing α-terpinene initially leads to an increase of ascaridole, indicating that the supply of singlet oxygen is in excess. Applying kinetic analysis, a pseudo first order reaction kinetics is confirmed, supporting this assumption. We have subsequently initiated a methodology of estimating the 1O2 concentrations based on the proportionality of ascaridole concentrations with respect to its maximum under these conditions. With the help of the estimated singlet oxygen data, the efficiency of 1O2 utilization and the photo efficiency of converting molecular oxygen to 1O2 are further proposed and evaluated. We have also identified conditions where further increase of α-terpinene has caused decreases in ascaridole, implying kinetically that 1O2 has now become a limiting reagent, the method of treating α-terpinene and ascaridole as a reaction pair in the data analysis would no longer be valid under those conditions.

: Oscillation synchronization through diffusion-based communication of active materials can lead to emergence of diverse patterns and collective behaviors. A detailed general description of the formation process of synchronization or resynchronization dynamics is a challenging task. We employ a photosensitive Belousov-Zhabotinsky reaction-diffusion model (within a gel media) to investigate the recovery process of oscillation synchronization between a pair of gel patches. The recovery time for oscillation resynchronization can be modulated by patch-distance, species of signaling molecules, intensity and duration of illumination. Analysis reveals that the “switch effect” of the gel-distance and the “promotion effect” from illumination on the oscillation resynchronization originate from the competition between processes of photo-promotion of oscillation, diffusion of signaling molecules (HBrO2 and Br-) and disproportionation of HBrO2. These results will benefit studies on bio-inspired active materials and soft motors.

: Efficient or at least rational use of energy resources is a problem that occupies an overwhelming number of people in modern society – from major scientists and politicians to journalists and schoolchildren who have a poor understanding of the basic laws of physics.(the knowledge of politicians in this area is also sometimes doubtful). At the same time, the main focus of the discussions is on the resource base, possible waste and consequences. According to these features, they want to see the future of energy. However, the division of "energetik" follows different principles. On the one hand, these are thermal, nuclear and hydropower sources. On the other – wind and solar energy. Obviously, this separation is not only related to the renewable resources or the absence of consequences for the environment and humans. If we do not touch on geopolitical problems. which are not the subject of this article, it is obvious that the main dividing feature of these types of energy production will be their controllability. The theory of automatic control (TAU) is one of the most complex modern sciences that has been developing for many years to solve precisely the problems of energy Now, when considering energy problems, this science is most often not remembered. Maybe because the most active participants in the discussions don't know much about it? Or is this situation beneficial to someone? How efficiency and controllability are related to some problems with controllability in the "household" energy sector, which concerns almost every inhabitant of the planet and in the global energy sector, this article is devoted to

Hydrogels, soft materials with 3D polymer networks in aqueous solution, have been developed for engineering and bio-related fields. However, these conventional hydrogels are weak and brittle due to lack of energy dissipation mechanisms. Recently, dual-network hydrogels have been proposed, combining rigid and flexible networks and exhibiting high strength, stretchability, and toughness. This paper explores the rheological properties of dual-network hydrogels based on acrylamide and sodium alginate under large deformations. This dual network is a combination of a covalently crosslinked polyacrylamide network and a supramolecular crosslinked sodium alginate network at the presence of divalent calcium cations. Small and large amplitude oscillatory shear methods with Fourier transform rheology, stress decomposition method, and Chebyshev polynomial analysis of large amplitude oscillatory shear (LAOS) data were employed to evaluate non-linearity limit, toughness, and network rigidity. The concentration of calcium ions affects (concentrations 0-80 mg/ml) the nonlinear transition and limit points, and all gel samples exhibit strain hardening, shear thickening, and shear densification.

This study considers the features of the chemical composition, internal structure, and oscillatory zoning of sulfides, sulfosalts and sulfates in the epithermal high-intermediate sulfidation type Au-Ag-Te Emmy deposit (Khabarovsk Territory), Russia. In this deposit the most widespread sulfide is pyrite occurring in two generations: pre-ore pure pyrite (I) with cubic crystal habit and dimensions from 20 μm to 0.5 mm from the early barren pre-ore hydrothermal stage, and pyrite (II) of the ore stage, which is represented by (a) colloform aggregates (IIa) formed as a result of rapid precipitation from the solution, and (b) crystalline pyrite (IIb), which is precipitated due to continuous decrease in temperature. Both pyrite (II) morphological varieties contain copper (0.06-6.03 wt.%). The crystalline variety of pyrite is associated with goldfieldite, hemusite and kawazulite which were deposited during the early mineralizing event in the deposit.

Electrical transmission between neurons is largely mediated by gap junctions. These junctions allow the direct flow of electric current between neurons, and in mammals are mostly composed of the protein connexin (Cx)36. Circuits of electrically coupled neurons are widespread in these animals, plus, experimental and theoretical evidence supports the notion that, beyond synchronicity, these circuits are able to perform sophisticated operations like lateral excitation and inhibition, noise reduction, as well as the ability to selectively respond upon coincident excitatory inputs. Although once considered stereotyped and unmodifiable, we now know that electrical synapses are subject to modulation and, by reconfiguring neural circuits, these modulations can alter relevant operations. The strength of electrical synapses depends on gap junction conductance, as well as on its functional interaction with the electrophysiological properties of coupled neurons. In particular, voltage dependent channels of the non-synaptic membrane critically determine the efficacy of transmission at these contacts. Consistently, modulatory actions on these channels have been shown to represent relevant mechanisms of plasticity of electrical synaptic transmission. Here we review recent evidence on the regulation of electrical synapses of mammals, the underlying molecular mechanisms, and the possible ways in which they affect circuit function.

Wall Shear Stress (WSS) abnormalities in carotid artery blood flow are key hemodynamic factors leading to arterial endothelial damage, atherosclerotic plaque formation, and carotid artery stenosis. Precise simulation of carotid artery blood flow WSS in vitro play an important role in understanding the underlying hemodynamic mechanism of carotid artery stenosis. This study presents a design for a microfluidic cell culture chamber with a variable cross-section and a step structure, leveraging microfluidic technology and principles of fluid dynamics. We propose an optimization strategy for microchannel dimensions based on Computational Fluid Dynamics (CFD) simulations. This strategy aims to replicate the distinct WSS waveform features found at various locations within the carotid bifurcation as observed in vivo. Our simulations indicate that with a step height of 0.09 mm, a width of 4 mm for the initial segment, and 5 mm for the subsequent wider channel, the device can effectively model the characteristics of low oscillatory WSS seen at sites of carotid sinus stenosis. Furthermore, it accurately represents the high-magnitude pulsatile WSS waveforms in the more uniform arterial sections downstream of the carotid sinus. The study also reveals that vortex formation and variations in low oscillatory WSS within the stepped section of the microchannel correlate with the step's height and width, as well as with the dimensions of the wider channel section. An increase in step width leads to a decrease in both the vortex area and the magnitude of negative WSS oscillations. When the step height is less than 0.03 mm, vortex formation is inhibited, challenging the simulation of low oscillatory WSS patterns. The variable cross-section microfluidic channel developed in this study provides a platform for simulating carotid artery WSS waveforms and facilitates research into the interplay between low oscillatory WSS at sites of carotid sinus stenosis and arterial endothelial dysfunction.

Keywords: flow mediated skin fluorescence; FMSF technique; NADH fluorescence, microcirculation, flowmotion, reactive hyperemia response, RHR, hypoxia sensitivity, HS, normoxia oscillatory index, NOI

The pulsatile flow rate (PFR) in the cerebral artery system and shunt ratios in bifurcated arteries are two patient-specific parameters which may affect the hemodynamic characteristics on the pathobiology of cerebral aneurysms (CAs). Accordingly, a systematic study was employed to investigate the effects of the two parameters on hemodynamic characteristics in two internal carotid artery sidewall aneurysms (i.e., ICASA-1 and ICASA-2) models. Numerical results indicate larger PFRs can cause higher WSS in some local regions of the aneurysmal dome that may increase the probability of small/secondary aneurysms generation than under smaller PFRs. The low WSS and relatively high oscillatory shear index (OSI) could appear under a smaller PFR, which has the potential to cause aneurysmal sac growth and rupture. However, the variances in PFRs and bifurcated shunt ratios have rare impacts on the time-average pressure distributions on the aneurysmal sac, although a higher PFR can contribute more to the pressure increase in ICASA-1 dome due to the relatively stronger impingement by the redirected blood stream than in ICASA-2. Simulation results also present the variances of shunt ratios have rare impacts on the hemodynamic characteristics in sacs, mainly because the bifurcated location is not close enough to the sac in present models. Furthermore, it has been found that the vortex location plays a major role in the temporal and spatial distribution of the WSS on the luminal wall, varying significantly with the cardiac period.