Angular Frequency Research Articles

Vibration of locally cracked pre-loaded parabolic arches

We study linear dynamics of an initially parabolic arch deformed by a uniform ‘dead’ load. The arch is seen as a fully deformable one-dimensional continuum with rigid cross-sections, one of which suffers from a small local crack at its boundary. The crack is simulated by springs, the stiffnesses of which are evaluated via stress intensity factors. By two first-order perturbations we investigate a non-trivial equilibrium adjacent to the reference configuration and small vibration superposed on it. The modulation of the initial load on the natural angular frequencies and its consequences on damage detection is described and commented. It turns out that neglecting the initial load, recalling for actual ‘dead’ structural actions, can be misleading in damage identification, while its inclusion leads to better results.

Experiments on an FM Mode-Locked Laser as an Arbitrary Optical Function Generator

We describe experimentally that an FM mode-locked laser can generate various optical pulses such as Gaussian, secant hyperbolic (sech), double-sided exponential, rectangular, parabolic, triangular, and Nyquist pulses like an optical function generator. The experiments were carried out by employing a 10 GHz actively FM mode-locked erbium fiber laser, where a specific filter was installed in the laser cavity. The specific filter was characterized by the Fourier transformed spectrum <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$A(\omega )$ </tex-math></inline-formula> of an output pulse <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$a(t)$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$A(\omega $ </tex-math></inline-formula> + <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n\Omega _{m})$ </tex-math></inline-formula> with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n=- \infty \sim + \infty $ </tex-math></inline-formula> . Here, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Omega _{m}$ </tex-math></inline-formula> is the angular modulation frequency. We employed a software-controlled liquid crystal on silicon (LCoS) optical filter, which can control the amplitude and the phase of the input signal as a function of optical frequency. Therefore, we were able to generate various optical pulses by simply changing the filter shape using the software. The filter resolution was 10 GHz. The generated optical pulses agreed well with the theory, where the spectral profile even below −40 dB coincided well with the theoretical profile. We proved experimentally from the product of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta \nu \Delta \tau $ </tex-math></inline-formula> at −3 dB that the output pulses have none of the frequency chirp that would inevitably occur with conventional FM mode-locking. It was not possible to generate an asymmetric single-sided pulse as we pointed out theoretically. We were also able to generate parabolic and triangular intensity pulses as we predicted in a previous paper. Finally, we compared the possibilities of generating various pulses with AM and FM mode-locking techniques.

Experiments on an AM Mode-Locked Laser as an Arbitrary Optical Function Generator

We show experimentally that various optical pulses can be generated from an AM mode-locked laser by employing a 10 GHz harmonically and regeneratively mode-locked erbium fiber laser. A software-controlled liquid crystal on silicon (LCoS) optical filter device, which can control the amplitude and phase of the input signal as a function of optical frequency, was employed to implement a specific filter function. The filter was characterized by the Fourier transformed spectral profile <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$A(\omega )$ </tex-math></inline-formula> of the output pulse <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$a(t)$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$A(\omega +\Omega _{m}), $ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$A(\omega -\Omega _{m})$ </tex-math></inline-formula> . Here, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Omega _{m}$ </tex-math></inline-formula> is the AM modulation angular frequency. The filter resolution was set at 10 GHz. By installing a specific filter in the laser cavity, we succeeded in generating various pulses such as Gaussian, secant hyperbolic (sech), double-sided and single-sided exponential, parabolic, triangular, and Nyquist pulses with an arbitrary roll-off factor as with an optical function generator. It is interesting to note that we could experimentally generate very precise transform-limited (TL) optical pulses, which were originally designed by calculating the filter function. The generated spectral profile agreed well with the numerical results even below −40 dB, which also agreed with the theory. As we have shown theoretically, we could generate sech and parabolic pulses without fiber nonlinearity. An asymmetric single-sided pulse can also be generated by incorporating a complex filter function with phase information, where a small amount of phase rotation of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sim \pi $ </tex-math></inline-formula> /60 in each round trip played an important role in generating the asymmetric pulse. Without the phase change, the pulse became symmetric and was no longer the designed pulse. A clean triangular pulse was difficult to generate since parabolic pulse shaping on the top of a sinusoidal intensity modulation is ineffective in creating a sharp peak.

Scattering amplitude and two-body loss of ultracold alkaline-earth atoms in a shaking synthetic magnetic field

The idea of manipulating the interaction between ultracold fermionic alkaline-earth (like) atoms via a laser-induced periodical synthetic magnetic field was proposed in Kanász-Nagy et al (2018 Phys. Rev. B 97, 155156). In that work, it was shown that in the presence of the shaking synthetic magnetic field, two atoms in 1S0 and 3P0 states experience a periodical interaction in a rotated frame, and the effective inter-atomic interaction was approximated as the time-averaged operator of this time-dependent interaction. This technique is supposed to be efficient for 173Yb atoms which have a large natural scattering length. Here we examine this time-averaging approximation and derive the rate of the two-body loss induced by the shaking of the synthetic magnetic field, by calculating the zero-energy inter-atomic scattering amplitude corresponding to the explicit periodical interaction. We find that for the typical cases with shaking angular frequency λ of the synthetic magnetic field being of the order of (2π) kHz, the time-averaging approximation is applicable only when the shaking amplitude is small enough. Moreover, the two-body loss rate increases with the shaking amplitude, and is of the order of 10−10 cm3 · s−1 or even larger when the time-averaging approximation is not applicable. Our results are helpful for the quantum simulations with ultracold gases of fermionic alkaline-earth (like) atoms.

The Influence of the Earth’s Atmosphere Rotation on the Spectrum of Acoustic-Gravity Waves

It was shown in a recent study [11] that taking into account the rotation of the Earth’s atmosphere leads to the appearance of a new region of evanescent waves with a continuous frequency spectrum on the diagnostic diagram of acoustic-gravity waves. The region is located below the lower limit of gravity waves, which is equal to $$2\Omega $$ for all wavelengths, where $$\Omega $$ is the angular frequency of the atmospheric rotation. This result was obtained for high-latitude regions of the atmosphere in which one can be limited to considering only the vertical component of the Earth’s rotation frequency. This paper shows that taking into account both components of the vector $$\vec {\Omega }$$ of the atmospheric rotation frequency $$\vec {\Omega }$$ —horizontal, $$\Omega \cos \varphi ,$$ where $$\varphi $$ is the local latitude, and vertical, $$\Omega \sin \varphi $$ —the dominant role in the acoustic-gravity wave propagation is played by the vertical component. It is shown that the horizontal component leads to a negligible modification of the boundaries of the regions of acoustic and gravity waves on the diagnostic diagram. It is also shown that the vertical component of the frequency affects most strongly the lower limit of gravity waves, which depends on the latitude of the observation site for all wavelengths and is equal to 2 $$\Omega \sin \varphi $$ .

ALMA-IMF

Aims.Thanks to the high angular resolution, sensitivity, image fidelity, and frequency coverage of ALMA, we aim to improve our understanding of star formation. One of the breakthroughs expected from ALMA, which is the basis of our Cycle 5 ALMA-IMF Large Program, is the question of the origin of the initial mass function (IMF) of stars. Here we present the ALMA-IMF protocluster selection, first results, and scientific prospects.Methods.ALMA-IMF imaged a total noncontiguous area of ~53 pc2, covering extreme, nearby protoclusters of the Milky Way. We observed 15 massive (2.5 −33 × 103M⊙), nearby (2−5.5 kpc) protoclusters that were selected to span relevant early protocluster evolutionary stages. Our 1.3 and 3 mm observations provide continuum images that are homogeneously sensitive to point-like cores with masses of ~0.2M⊙and ~0.6M⊙, respectively, with a matched spatial resolution of ~2000 au across the sample at both wavelengths. Moreover, with the broad spectral coverage provided by ALMA, we detect lines that probe the ionized and molecular gas, as well as complex molecules. Taken together, these data probe the protocluster structure, kinematics, chemistry, and feedback over scales from clouds to filaments to cores.Results.We classify ALMA-IMF protoclusters as Young (six protoclusters), Intermediate (five protoclusters), or Evolved (four proto-clusters) based on the amount of dense gas in the cloud that has potentially been impacted by H IIregion(s). The ALMA-IMF catalog contains ~700 cores that span a mass range of ~0.15M⊙to ~250M⊙at a typical size of ~2100 au. We show that this core sample has no significant distance bias and can be used to build core mass functions (CMFs) at similar physical scales. Significant gas motions, which we highlight here in the G353.41 region, are traced down to core scales and can be used to look for inflowing gas streamers and to quantify the impact of the possible associated core mass growth on the shape of the CMF with time. Our first analysis does not reveal any significant evolution of the matter concentration from clouds to cores (i.e., from 1 pc to 0.01 pc scales) or from the youngest to more evolved protoclusters, indicating that cloud dynamical evolution and stellar feedback have for the moment only had a slight effect on the structure of high-density gas in our sample. Furthermore, the first-look analysis of the line richness toward bright cores indicates that the survey encompasses several tens of hot cores, of which we highlight the most massive in the G351.77 cloud. Their homogeneous characterization can be used to constrain the emerging molecular complexity in protostars of high to intermediate masses.Conclusions.The ALMA-IMF Large Program is uniquely designed to transform our understanding of the IMF origin, taking the effects of cloud characteristics and evolution into account. It will provide the community with an unprecedented database with a high legacy value for protocluster clouds, filaments, cores, hot cores, outflows, inflows, and stellar clusters studies.

FAULT DETECTION INSPECTION ANALYSIS OF A GAS TURBINE USING FREQUENCY DOMAIN

Analysing torsional vibration (TV) of the rotor shaft system can mitigate long down times and high maintenance cost. TV analysis can also eliminate faults such as shaft crack, coupling misalignment and rotor imbalance are some of the common causes of TV in the gas turbine (GT). The rotor shaft is a major mechanical component of the gas turbine engine (GTE) responsible for power generation and power transformation. Reliability and performance of the system is mostly determined by the efficiencies of the rotor system. This research therefore presents a computer based analytical solution method for TV to be used in fault detection. In arriving at the method, a single degree of freedom system was modeled and relevant equations were derived. These equations was programmed using Matlab and results was implemented with the data of an operational existing plant. It was discovered that input parameters such as norminal speed 3000 rpm, spring stiffness is 200 GN/mm, mass moment of inertial 22071.5 kgm2 and optimum power capacity is 125 mW. The software developed in this research will be useful for training in tertiary institutions and easy for both technical and non-technical personnel on TV analysis of GTE. A total of 5*10-11m, 4.3 *10-10 m/s and 1.4*10-10 m/s2 is shown as the angular displacement, velocity and acceleration. An angular frequency of 314 to 320 hertz was used in this analysis. It was observed that the GT used in this analysis is fairly new and therefore healthy. No fault was detected and values of angular displacement, velocity and acceleration was observed to be relatively small.

Motion of charged and spinning particles influenced by dark matter field surrounding a charged dyonic black hole

We investigate the motion of massive charged and spinning test particles around a charged dyonic black hole spacetime surrounded by perfect fluid scalar dark matter field. We obtain the equations of motion and find the expressions for the four-velocity for the case of a charged particle, and four-momentum components for the case of a spinning particle. The trajectories for various values of electric $Q_{e}$ and magnetic $Q_{m}$ charges are investigated under the influence of dark matter field $\lambda$. We find the equations of motion of a spinning particle that follows a non-geodesic trajectory via Lagrangian approach in addition to the charged and non-spinning particles that follow geodesic motion in this set-up. We study in detail the properties of innermost stable circular orbits (ISCOs) in the equatorial plane. The study of ISCOs of a spinning massive particle is done by using the pole-dipole approximation. We show that, in addition to the particle's spin, the dark matter field parameter $\lambda$ and black hole charges ($Q_{m}\;\text{and}\;Q_{e}$) have a significant influence on the ISCOs of spinning particles. It is observed that if the spin is parallel to the total angular momentum $J$ (i.e. $\mathcal{S}>0$), the ISCO parameters (i.e.$r_{ISCO}, L_{ISCO}\;\text{and}\; E_{ISCO}$) of a spinning particle are smaller than those of a non-spinning particle, whereas if the spin is anti-parallel to total angular momentum $J$ (i.e. $\mathcal{S}<0$), the value of the ISCO parameters is greater than that of the non-spinning particle. We also show that for the corresponding values of spin parameter S, the behaviour of Keplerian angular frequency of ISCO $\Omega_{ISCO}$ is opposite to that of $r_{ISCO}, L_{ISCO}\; \text{and}\; E_{ISCO}$.

AC response of spin-pseudospin current in a double quantum well

The spin Hall effect due to the skew scattering is studied using the Boltzmann equation in a double quantum well when the inplane electric field with angular frequency ω is applied. The two wells have opposite signs of impurity potential so that the skew-scattering spin Hall current is antiparallel and carries a pseudospin, which is formed by ∣L〉 and ∣R〉, the ground states of the two wells. The pseudospin precession is induced by the interwell tunneling in the strength of ℏ ω SAS, the energy difference between the symmetric and antisymmetric states. It is found that the dynamics of the spin-pseudospin current, described by the pseudospin analogue of the Bloch equation, is equivalent in form to the classical cyclotron resonance. Consequently, the antiparallel spin Hall current exhibits the resonance peak at ω ∼ ω SAS. Such spin-pseudospin coupling is expected to be useful in controlling the spin polarization in many electronic systems.

Modified viscoelastic wavefield simulations in the time domain using the new fractional Laplacians

Abstract Accurately characterizing seismic attenuation effects on wave propagations is crucially important for structure interpretation and reservoir evaluation. The conventional fractional viscoelastic wave equation is not satisfactory on accuracy for small Q values. To solve this issue, we derive a novel fractional viscoelastic wave equation by combining an accurate relationship between angular frequency and complex wavenumber. The dissipation- and dispersion-dominated wave equations are also derived to simulate the amplitude-dissipation and phase-dispersion characteristics. The truncated Taylor-series expansion (TE) algorithm is developed to approximate the mixed-domain operators. After that, the generalized pseudospectral approach can be directly used to solve the new wave equation. In addition, an accurate viscoelastic wave equation constructed by the fractional time derivatives is used to calculate reference solutions to evaluate the accuracy of the new expression. Modelling results indicate that the newly proposed viscoelastic wave equation using the new fractional Laplacians is more accurate than the conventional one, especially in a small Q medium (i.e. QP = QS = 5). Furthermore, we also examine the accuracy of the TE approximation with a series of Q values. A homogeneous model and the modified BP2004 viscoelastic model are used to investigate the accuracy of viscoelastic wave propagations using the TE algorithm. All modelling results fully demonstrate the performance of the newly proposed viscoelastic wave equation and numerical algorithm.

Effects of homojunction on the reflected and transmitted waves at the interface between two thermoelastic semiconductor half spaces

It is systematically investigated that the influence of interface effect resulted from one homojunction on the reflected and transmitted thermoelastic waves between two bonded homogeneous isotropic thermoelastic semiconductor half spaces in this paper. Considering the geometrical and physical characteristics of homojunction, it is approximately treated as a two-dimensional isotropic imperfect interface without geometrical thickness mathematically but with elastic, thermal and semiconductor properties depicted through a dimensionless characteristic length factor physically. Considering the coupling effect of mechanical displacement, temperature change and charge carrier concentration perturbation, the imperfect interface boundary condition is established based on the generalized Green-Naghdi theory, the surface and interface elastic theory and the physical property of homojunction. The algebraic equation resulted from this imperfect interface boundary condition is solved to obtain the reflected and transmitted coefficients of thermoelastic waves expressed in the energy flux ratio, which are verified by the principle of energy conservation. The numerical calculation results demonstrate that the increase of geometrical thickness of homojunction and the angular frequency of thermoelastic waves can enhance the interface imperfect property and arise more evident influence of interface effect. Meanwhile, the interface effect has a more evident influence on the thermoelastic waves propagating along the interface normal direction. The physical mechanism revealed through the establishment of mathematical model provides a theoretical basis for using PN junction to regulate the propagation properties of thermoelastic waves in thermoelastic semiconductors.

Memory Response on the Elasto-Thermodiffusive Interaction Subjected to Harmonically Varying Heat Source

Enlightened by the Caputo type of fractional derivative, this research paper is the analysis of a mathematical model of generalized thermoelastic diffusion with memory-dependent derivative (MDD) for an isotropic infinite medium with a cylindrical cavity in the context of dual-phase lag model. The surface of the cavity is traction free and subjected to harmonically heat sources with constant angular frequency of thermal vibration. Laplace transform technique has been used to solve the problem. Later eigenvalue approach is used to obtain the analytical expressions for different physical fields in the transformed domain. Finally to obtain the solutions in the real-time domain, the Riemann-sum approximation method is used. According to the graphical representations corresponding to the numerical results, the effect of heat source speed on temperature, displacement, stress, mass concentration and chemical potential are studied. The effect of memory-dependent parameters, as well as in the absence of MDD on physical quantities are also demonstrated.

Electro-rotation of spheroids in fluids under linear-polarized AC electric field: A dynamic model

Under a linear-polarized AC electric field, a spheroid suspended in fluids typically aligns one of its axes with the field. The time-averaged torque model is widely used to predict the orientation of the spheroid with respect to the field. Different from the AC case, the dynamical behaviors including stable orientation, stable spinning, and the limit cycle of spheroids under the DC electric field are much richer. An inconsistency exists between the two cases, and a criterion for the validity of the time-average torque model is also missing. In this article, the dynamic model for the DC electric field was adapted to its AC counterpart and the full dynamics of spheroids under the AC field were studied. We bridged the DC and AC dynamics of spheroidal particles and widened the frequency range for applying the time-averaged torque model. It was found that the phase diagram at the DC limit is a very instructive guiding map for predicting the dynamical behavior at the AC field and ωτη ∼ 1 (ω: angular frequency of the electric field, τη: characteristic time of particle rotation) appears to be a universal criterion for the time-averaged model to be effective. The flipping of particle orientation was explained with bifurcations of the periodic solutions and the irregular dynamics at low frequencies were uncovered with the Poincaré map and the power spectrum analysis. Our study sheds light on even richer dynamical behaviors of the particles under the AC electric field and may help realize other unconventional dynamical behaviors of particles in the future.

Methods on the Determination of the Circuit Parameters in an Underwater Spark Discharge

We constructed an underwater discharge system to conduct a number of experiments. Considering the constant resistance of the plasma channel, we got an analytic expression for the current containing unknown parameters on the basis of the Kirchhoff voltage law. Therefore, we are required to determine the total circuit resistance R with the measured current data in hand. Three methods are employed to get this job done, namely, nonlinear least squares with three variables (NLS-TV), nonlinear least squares with a single variable (NLS-SV), and waveform calculation method (WCM). The Levenberg–Marquardt (L-M) algorithm and particle swarm optimization (PSO) algorithm are employed in NLS-TV and NLS-SV, and the root mean square error (RMSE), as well as an improved cosine similarity (ICS), was selected to evaluate the performance of algorithms. The results show that NLS-TV gives an optimal solution with the combination of the PSO algorithm and L-M algorithm. Then, by calculation, R = 1.3195 Ω , C = 0.56865 μF, and L = 17.172 μH. RMSE and ICS between fitted current data and measured one are 43.9689 and 0.9947, respectively. NLS-SV gives a satisfying solution either by PSO or by L-M, yet it needs information of angular frequency from the measured current waveform and the total inductance C . In this case, we get R = 1.3115 Ω , L = 16.969 μH, RMSE = 48.0883, and ICS = 0.9967. As for WCM, it is completely dependent on the measured current waveform and the total inductance C . The corresponding values of R and L are 1.2463 Ω and 16.993 μH. Also, we get RMSE = 52.1902 and ICS = 0.9728. For NLS-SV and WCM, the needed total capacitance during calculation is determined using the computed capacitance by NLS-TV. If the energy storage capacitance is used as the total capacitance, the obtained solution is frustrating. Therefore, independent use of NLS-SV or WCM demands a precise capacitance of the total circuit measured by an RLC meter. We also draw a conclusion that ignoring the capacitance of other parts of the circuit is incorrect and will lead to an enormous error during calculation.

Rheological model for the alpha relaxation of glass-forming liquids and its comparison to data for DC704 and DC705.

Dynamic shear-modulus data are presented for two silicone oils DC704 and DC705 for frequencies between 1 mHz and 10kHz at temperatures covering more than five decades of relaxation-time variation. Data are fitted to the alpha part of a phenomenological model previously shown to describe well the dynamic shear modulus of squalane, which has a large beta process [Hecksher et al., J. Chem. Phys. 146, 154504 (2017)]. That model is characterized by additivity of the alpha and beta shear compliance and by a high-frequency decay of the alpha process in proportion to ω-1/2, where ω is the angular frequency. The fits of the alpha part of this model to the DC704 and DC705 data are compared to fits by a Havriliak-Negami type model, a Barlow-Erginsav-Lamb model, and a Cole-Davidson type model. At all temperatures, the best fit is obtained by the alpha part of the squalane model. This strengthens the conjecture that so-called t-relaxation, leading to high-frequency loss decays proportional to ω-1/2, is generic to the alpha relaxation of supercooled liquids [J. C. Dyre, Phys. Rev. E 74, 021502 (2006); Nielsen et al., J. Chem. Phys. 130, 154508 (2009); and Pabst et al., J. Phys. Chem. Lett. 12, 3685-3690 (2021)].

Field-Induced Viscoelastic and Creep and Recovery Behavior of Water-Based MR Fluids Using Bentonite and Oleic Acid as an Additive

The viscoelastic and creep and recovery behaviors of a carbonyl iron (CI)-water-based magnetorheological fluid (MRF) were studied under dynamic and constant loading conditions. The feature of MR fluid is to change from liquid to semi-solid state just in a few milliseconds after applying a magnetic field. ThereforeMR fluid is a kind of smart material whose rheological properties change with step-change in a magnetic field. We prepared MR fluids comprising CI 65 wt%, water 35 wt %, bentonite 3 wt %, and oleic acid 1 wt %. Because bentonite with nanosized fills the voids between the CI particles, it was used with oleic acid to enhance the MR response of the CI/water suspension. The strain amplitude tests reveal that MR fluid behaves as a viscoelastic material in the LVE range and a transition of fluid occurred from linear viscoelastic to non-linear viscoelastic behavior at the critical strain of 0.1%. Its storage moduli confirmed a steady plateau region for the entire angular frequency range, suggesting the well-known solid-like behavior of the MR suspension. The creep and recovery result signified that as the magnetic field increased, the instantaneous creep strain contributions decreased dramatically.

Alkali metals in the attosecond pulse train

The problem of sodium and potassium in the attosecond pulse train (APT) as a kicking field is considered. The goal is to investigate the possibility of the kicking field to generate, in general, any secondary radiation. The modifications of the energy bands and the kick-induced currents are examined. Simple local pseudopotentials have been proposed and used. It is demonstrated that the APT generates secondary radiation in a wider spectral range similar to high-order harmonic generation (HHG). This radiation has been found to have a form of periodic complex peak compositions decreasing in intensity with the period approximately equal to the doubled angular frequency of the driving field. This is a new effect. A physical explanation of this effect is given.

Buoyant flow instability induced by a uniform internal heat source in a vertical annular porous layer

The buoyancy–induced parallel flow in a vertical cylindrical porous layer with annular cross–section is analysed. A radial thermal gradient caused by a uniformly distributed heat source is assumed to induce the buoyant flow. The layer boundaries are modelled as isothermal and permeable to an external fluid reservoir. The onset of the convective instability is analysed by linearising the governing equations for the perturbations. The governing parameters driving the instability are the heat–source Rayleigh number and the ratio between the internal radius and the external radius. Neutral stability curves and the critical values of the Rayleigh number, the perturbation wave number and the angular frequency are computed numerically. It is shown that axisymmetric modes form the most dangerous type of instability.

Melt-state degradation mechanism of poly (ether ketone ketone): the role of branching on crystallization and rheological behavior

In the melt-state, poly (ether ketone ketone) (PEKK) undergoes structural changes to the polymer backbone due to its high melting temperature. In this work, the thermal degradation mechanism of PEKK in the melt-state in air is identified using a combination of molecular dynamics (MD) simulations, X-ray photoelectron spectroscopy (XPS), and rheology. Ether linkages in the PEKK backbone are shown to have the lowest bond dissociation energies and preferentially undergo chain scission compared to ketone linkages. Upon chain scission, the formed radical species undergo hydrogen abstraction, chain transfer, and a coupling reaction, resulting in altered viscoelastic properties. Dynamic rheological behavior of PEKK thermally aged in the melt-state display viscoelastic characteristics of long-chain branched polymers. Results indicate that the PEKK rheological properties are highly dependent on time in the melt-state as well as angular frequency. Increased exposure times in the melt-state result in increased complex viscosity and a reduction in the degree and rate of crystallization. Thermal history has a significant impact on thermomechanical properties in the melt-state and during crystallization.

Measuring Active Power as the Difference between the Peak Value of Instantaneous Power and the Apparent Power

The traditional approach to calculate the active and reactive power in AC power systems requires the measurement of the phase shift between the voltage and current for the evaluation of the power factor. To do this, power analyzers can implement several methods. In principle, it is always necessary to identify specific points of waveforms (e.g., using a zero-crossing detection technique) and get their time shift. In a similar way, the frequency value must be evaluated in order to calculate the angular frequency. Unfortunately, this kind of common method exhibits some issues, such as the large sensitivity to noise. Moreover, inaccuracies in the evaluation of the power factor have a big impact on the final estimation of the electric power. This paper presents a simple but effective way to calculate the electric power, overcoming the need for a direct measurement of the phase shift and frequency. In particular, it is shown that the active power can be easily calculated as the difference between the peak value of the instantaneous power and apparent power. The reactive power and power factor are evaluated by exploiting the same quantities. The practical implementation of the proposed formulation in power analyzers guarantees several benefits without reducing accuracy.