Thermal Damping of Weak Magnetosonic Turbulence in the Interstellar Medium

We present a generic mechanism for the thermal damping of compressive waves in the interstellar medium (ISM), occurring due to radiative cooling. We solve for the dispersion relation of magnetosonic waves in a two-fluid (ion-neutral) system in which density- and temperature-dependent heating and cooling mechanisms are present. We use this dispersion relation, in addition to an analytic approximation for the nonlinear turbulent cascade, to model dissipation of weak magnetosonic turbulence. We show that in some ISM conditions, the cutoff wavelength for magnetosonic turbulence becomes tens to hundreds of times larger when the thermal damping is added to the regular ion-neutral damping. We also run numerical simulations, which confirm that this effect has a dramatic impact on cascade of compressive wave modes.

Lateral resolution limit of laser Doppler vibrometer microscopes for the measurement of surface acoustic waves

The lateral or transverse resolution of single-point interferometers for vibration measurement is especially critical for microelectromechanical systems (MEMS) vibrating up to the gigahertz range. In this regime, the acoustic wavelengths are typically in the range of the size of the laser focus. Thus, a successful vibration measurement requires distinct knowledge about the lateral resolution limit and its dependencies with instrumentation parameters. In this paper, we derive an analytic approximation formula, which allows for estimation of the systematic measurement deviation of the vibration amplitude and, thus, a definition of the lateral resolution limit of single-point interferometers for vibration measurement. Further, a compensation and an optimum numerical aperture are proposed the reduce the measurement deviation. For this, the model includes a laser-interferometer microscope of Mach-Zehnder type with Gaussian laser beams considering the Gouy effect and wavefront curvature. As a measurement scenario, an unidirectional surface acoustic wave (SAW) is regarded. The theoretic findings have been validated in the experiment with a representative vibration measurement on a SAW filter at $$433\,{\mathrm {MHz}}$$ 433 MHz with our heterodyne laser-Doppler interferometer with offset-locked semiconductor lasers. The provided formulas help instrument designers and users to choose suitable instrument parameters, especially the numerical aperture of the utilized microscope objective.

Research on 3D SIP Conjugate Gradient Inversion Algorithm with Parameter Range Constraints

3D SIP inversion algorithm involves multiple parameters, and the key is the calculating speed and memory. A whole set of quasi-linear (QL) theories has taken shape in recent years, including the QL approximation method proposed by Zhdanov, quasi-analytic approximation, and localized quasi-linear (LQL) approximation. They are characterized by high speed and accuracy in electromagnetic field numerical modeling. The above-based 3D QL inversion algorithm, boasting quicker calculating speed plus more stable and favorable inversion effect, has been adopted profoundly in electromagnetic prospecting, whereas its frequent source conversion requires recalculating the dyadic Green’s function and primary field each time, thus delaying the 3D SIP modeling speed. This study makes use of the spatial symmetry in the primary field and Green function to propose an effective and quicker QL forward modeling method, which has the hallmark of higher calculating speed owing to less calculating times, and makes feasible the 3D SIP conjugate gradient inversion algorithm with Cole–Cole parameter range constraints.

Memristor Circuits for Simulating Neuron Spiking and Burst Phenomena

Since the introduction of memristors, it has been widely recognized that they can be successfully employed as synapses in neuromorphic circuits. This paper focuses on showing that memristor circuits can be also used for mimicking some features of the dynamics exhibited by neurons in response to an external stimulus. The proposed approach relies on exploiting multistability of memristor circuits, i.e., the coexistence of infinitely many attractors, and employing a suitable pulse-programmed input for switching among the different attractors. Specifically, it is first shown that a circuit composed of a resistor, an inductor, a capacitor and an ideal charge-controlled memristor displays infinitely many stable equilibrium points and limit cycles, each one pertaining to a planar invariant manifold. Moreover, each limit cycle is approximated via a first-order periodic approximation analytically obtained via the Describing Function (DF) method, a well-known technique in the Harmonic Balance (HB) context. Then, it is shown that the memristor charge is capable to mimic some simplified models of the neuron response when an external independent pulse-programmed current source is introduced in the circuit. The memristor charge behavior is generated via the concatenation of convergent and oscillatory behaviors which are obtained by switching between equilibrium points and limit cycles via a properly designed pulse timing of the current source. The design procedure takes also into account some relationships between the pulse features and the circuit parameters which are derived exploiting the analytic approximation of the limit cycles obtained via the DF method.

Deriving the dark matter-dark energy interaction term in the continuity equation from the Boltzmann equation

Dark energy and dark matter are two of the biggest mysteries of modern cosmology, and our understanding of their fundamental nature is incomplete. Many parametrizations of couplings between the two in the continuity equation have been studied in the literature, and observational data from the growth of perturbations can constrain these parametrizations. Assuming standard general relativity with a simple Yukawa-type coupling between dark energy and dark matter fields in the Lagrangian, we use the Boltzmann equation to analytically express and calculate the interaction kernel Q in the continuity equation and compare it to that of a typical parametrization. We arrive at a comparably very small result, as expected. Since the interaction is a function of the dark matter mass, other observational data sets can be used to constrain the mass. This calculation can be modified to account for other couplings of the dark energy and dark matter fields. This calculation required obtaining a distribution function for dark energy that leads to an equation of state parameter that is negative, which neither Bose–Einstein nor Fermi–Dirac statistics can supply, and this is the main result of this paper. Treating dark energy as a quantum scalar field, we use adiabatic subtraction to obtain a finite analytic approximation for its distribution function that assumes the FLRW metric and nothing more.

Accurate analytic approximation for the Chapman grazing incidence function

A new analytical approximation for the Chapman mapping integral, $${\text {Ch}}$$ Ch , for exponential atmospheres is proposed. This formulation is based on the derived relation of the Chapman function to several classes of the incomplete Bessel functions. Application of the uniform asymptotic expansion to the incomplete Bessel functions allowed us to establish the precise analytical approximation to $${\text {Ch}}$$ Ch , which outperforms established analytical results. In this way the resource consuming numerical integration can be replaced by the derived approximation with higher accuracy. The obtained results are useful for various branches of atmospheric physics such as the calculations of optical depths in exponential atmospheres at large grazing angles, physical and chemical aeronomy, atmospheric optics, ionospheric modeling, and radiative transfer theory.