Dynamic vortex evolution of harmonically trapped coupled Bose–Einstein condensate with quintic nonlinearity

In this study, we investigate the evolution of vortex in harmonically trapped two-component coupled Bose–Einstein condensate with quintic-order nonlinearity. We derive the vortex solution of this two-component system based on the coupled quintic-order Gross–Pitaevskii equation model and the variational method. It is found that the evolution of vortex is a metastable state. The radius of vortex soliton shrinks and expands with time, resulting in periodic breathing oscillation, and the angular frequency of the breathing oscillation is twice the value of the harmonic trapping frequency under infinitesimal nonlinear strength. At the same time, it is also found that the higher-order nonlinear term has a quantitative effect rather than a qualitative impact on the oscillation period. With practical experimental setting, we identify the quasi-stable oscillation of the derived vortex evolution mode and illustrated its features graphically. The theoretical results developed in this work can be used to guide the experimental observation of the vortex phenomenon in ultracold coupled atomic systems with quintic-order nonlinearity.

Thermoelastic Coupling Response of an Unbounded Solid with a Cylindrical Cavity Due to a Moving Heat Source

The current article introduces the thermoelastic coupled response of an unbounded solid with a cylindrical hole under a traveling heat source and harmonically altering heat. A refined dual-phase-lag thermoelasticity theory is used for this purpose. A generalized thermoelastic coupled solution is developed by using Laplace’s transforms technique. Field quantities are graphically displayed and discussed to illustrate the effects of heat source, phase-lag parameters, and the angular frequency of thermal vibration on the field quantities. Some comparisons are made with and without the inclusion of a moving heat source. The outcomes described here using the refined dual-phase-lag thermoelasticity theory are the most accurate and are provided as benchmarks for other researchers.

Electronically Tunable TISO Voltage-Mode Universal Filter Using Two LT1228s

This study aims to design an electronically tunable voltage-mode (VM) universal filter utilizing commercially available LT1228 integrated circuits (ICs) with three-input and single-output (TISO) configuration. With the procedure based on two integrator loop filtering structures, the proposed filter consists of two LT1228s, four resistors, and two grounded capacitors. It realizes five filter output responses: low-pass, all-pass, band-reject, band-pass, and high-pass functions. By selecting input voltage signals, each output responses can be achieved without changing the circuit architecture. The natural angular frequency can be controlled electronically. The input voltage nodes Vin1 and Vin3 possess high impedance. The output node has low impedance, so it can be cascaded to other circuits. The performance of the proposed filter is corroborated by PSpice simulation and hardware implementation which support the theoretical assumptions. The result shows that the range of total harmonic distortion (THD) is lower than 1%, and that the higher the temperature is, the lower the natural angular frequency is.

A Sharp Version of Price’s Law for Wave Decay on Asymptotically Flat Spacetimes

We prove Price’s law with an explicit leading order term for solutions $$\phi (t,x)$$ ϕ ( t , x ) of the scalar wave equation on a class of stationary asymptotically flat $$(3+1)$$ ( 3 + 1 ) -dimensional spacetimes including subextremal Kerr black holes. Our precise asymptotics in the full forward causal cone imply in particular that $$\phi (t,x)=c t^{-3}+{\mathcal {O}}(t^{-4+})$$ ϕ ( t , x ) = c t - 3 + O ( t - 4 + ) for bounded |x|, where $$c\in {\mathbb {C}}$$ c ∈ C is an explicit constant. This decay also holds along the event horizon on Kerr spacetimes and thus renders a result by Luk–Sbierski on the linear scalar instability of the Cauchy horizon unconditional. We moreover prove inverse quadratic decay of the radiation field, with explicit leading order term. We establish analogous results for scattering by stationary potentials with inverse cubic spatial decay. On the Schwarzschild spacetime, we prove pointwise $$t^{-2 l-3}$$ t - 2 l - 3 decay for waves with angular frequency at least l, and $$t^{-2 l-4}$$ t - 2 l - 4 decay for waves which are in addition initially static. This definitively settles Price’s law for linear scalar waves in full generality. The heart of the proof is the analysis of the resolvent at low energies. Rather than constructing its Schwartz kernel explicitly, we proceed more directly using the geometric microlocal approach to the limiting absorption principle pioneered by Melrose and recently extended to the zero energy limit by Vasy.

Ancient Wheat and Quinoa Flours as Ingredients for Pasta Dough—Evaluation of Thermal and Rheological Properties

The aim of this study was to investigate thermal and rheological properties of selected ancient grain flours and to evaluate rheological properties of mixtures thereof represented by pasta dough and dry pasta. Flours from spelt, einkorn, and emmer ancient wheat varieties were combined with quinoa flour. All these flour sources are considered healthy grains of high bioactive component content. Research results were compared to durum wheat flour or spelt wheat flour systems. Differential scanning calorimeter (DSC) and a rapid visco analyzer (RVA) were used to investigate the phase transition behavior of the flours and pasting characteristics of the flours and dried pasta. Angular frequency sweep experiments and creep and recovery tests of the pasta dough were performed. The main components modifying the pasta dough structure were starch and water. Moreover, the proportion of the individual flours influenced the rheological properties of the dough. The durum wheat dough was characterized by the lowest values of the K′ and K″ parameters of the power law models (24,861 Pa·sn′ and 10,687 Pa·sn″, respectively) and the highest values of the instantaneous (J0) and retardation (J1) compliances (0.453 × 10−4 Pa and 0.644 × 10−4 Pa, respectively). Replacing the spelt wheat flour with the other ancient wheat flours and quinoa flour increased the proportion of elastic properties and decreased values of the J0 and J1 of the pasta dough. Presence of the quinoa flour increased pasting temperature (from 81.4 up to 83.3 °C) and significantly influenced pasting viscosities of the spelt wheat pasta samples. This study indicates a potential for using mixtures of spelt, einkorn, and emmer wheat flours with quinoa flour in the production of innovative pasta dough and pasta products.

Theoretical and Experimental Study of Current from Non-Disintegrable Suspended Particles at a Rotating Disk Electrode

Understanding the current response at an electrode from suspended solid particles in an electrolyte is crucial for developing materials to be used in semi-solid electrodes for energy storage applications. Here, an analytical model is proposed to predict and understand the current response from non-disintegrable solid particles at a rotating disk electrode. The current is shown to be limited by a combination of ion diffusion within the solid particle and the mean residence time of the particle at the rotating disk electrode. This results in a relationship between current and angular frequency of I∝ω^(3/4), instead of the classical I∝ω^(1/2) predicted by Levich theory. Specifically, the current response of Li4Ti5O12 (LTO) microparticles suspended in a non-aqueous electrolyte of lithium hexafluorophosphate (LiPF6) in ethylene carbonate: diethyl carbonate (EC:DEC) was determined experimentally and compared favorably with predictions from the proposed analytical model using fitting parameters consistent with the experimental conditions.

The Echo Method for Axion Dark Matter Detection

The axion is a dark matter candidate arising from the spontaneous breaking of the Peccei–Quinn symmetry, introduced to solve the strong CP problem. It has been shown that radio/microwave radiation sent out to space is backscattered in the presence of axion dark matter due to stimulated axion decay. This backscattering is a feeble and narrow echo signal centered at an angular frequency very close to one-half of the axion mass. In this article, we summarize all the relevant results found so far, including analytical formulas for the echo signal, as well as sensitivity prospects for possible near-future experiments.

Frequency characteristics of dissipative and generative fractional RLC circuits

Equations governing the transient and steady-state regimes of the fractional series RLC circuits containing dissipative and/or generative capacitor and inductor are posed by considering the electric current as a response to electromotive force. Further, fractional RLC circuits are analyzed in the steady-state regime and their energy consumption/production properties are established depending on the angular frequency of electromotive force. Frequency characteristics of the modulus and argument of transfer function, i.e., of circuit's equivalent admittance, are analyzed through the Bode diagrams for the whole frequency range, as well as for low and high frequencies as the asymptotic expansions of transfer function modulus and argument.

Study of a Stripper Header for Grain Harvesting as a Vibrating System

Introduction. Grain losses caused by stripping defects are the main problem to be solved in designing a stripper header. To reduce these losses, a design of a stripper header with a vibration drive is proposed. This device combines the processes of stripping grain crops and the vibration effect of the stripping fingers upon the ears of plants. The most important stage of the mathematical description of these processes is composing the differential equation of the stripping fingers motion. Materials and Methods. A computational-graphic diagram of an oscillatory system with one degree of freedom is proposed. To compose the differential equation of the stripping fingers motion, a method based on the application of the Lagrange equation was used. The oscillations of the system under studying arise from the motion of a point in the system according to a given law. The problem of kinematic excitation is reduced to the problem of force perturbation. This stage of the study was carried out without taking into account the resistance forces. Results. An equation for motion of stripping fingers making vibrational reciprocating movements is obtained. It is proposed to select the elastic element in the design scheme and consider a more general case of the stripping fingers movement. In this case, the movement of the stripping fingers is considered to be difficult. A characteristic feature of the mathematical description is the presence of a generalized force of potential forces. The differential equation of motion of a comb in the presence of an elastic element and the solution of this equation are composed. Discussion and Conclusion. Forced oscillations of a system without resistance, excited by a harmonic disturbing force, are harmonic oscillations with constant amplitude. On close values of the angular frequency of vibration of the drive output link and the root of the ratio of the stiffness coefficient of the elastic element to the stripping fingers mass, the case of resonance takes place. The system parameters must be selected so as to avoid this negative phenomenon.

Singular Nonlinear Equation Class : Theoretical and Experimental Concept

This work generalizes and extends our work in refs [10,29,37], dealing a theoretical model of a monoatomic chain immersed in a potential of periodic and deformable substrate, the third and fourth non-linearities being taken into account. Looking at the analytical localized modes provides an extended interpretation of system dynamics based upon modes existence and yields an extended form of the nonlinear Schrodinger equation to describe the eikonal wave's complex amplitude. In this equation, the coeffcients depend on the wavenumber, whereas the parallel with the nonlinear transmission electrical line introduced in references results in [1,2] not fully resolved dynamic equations. So far, only specific solutions have been presented. Our dynamic study thus presents a theoretical prediction for their experimental set up. In contrast to previous works done for particular values of the wavenumber, namely on the behavior of gap (k = 0 and k = π) solutions of the model [10], or for k (k = ±2π=3) in the central bandpass area [37], we consider here rather behaviors of the system when the angular frequency is arbitrary. By using bifurcation theory of planar dynamical systems and investigating the dynamical behavior, we derive a variety of solutions corresponding to the phase trajectories under different parameter conditions.