Real Frequency Research Articles

SmoQyDEAC.jl: A differential evolution package for the analytic continuation of imaginary time correlation functions

We introduce the SmoQyDEAC.jl package, a Julia implementation of the Differential Evolution Analytic Continuation (DEAC) algorithm [N. S. Nichols et al., Phys. Rev. E 106, 025312 (2022)] for analytically continuing noisy imaginary time correlation functions to the real frequency axis. Our implementation supports fermionic and bosonic correlation functions on either the imaginary time or Matsubara frequency axes, and treatment of the covariance error in the input data. This paper presents an overview of the DEAC algorithm and the features implemented in the SmoQyDEAC.jl package. It also provides detailed benchmarks of the package’s output against the popular maximum entropy and stochastic analytic continuation methods. The code for this package can be downloaded from our GitHub repository at https://github.com/SmoQySuite/SmoQyDEAC.jl or installed using the Julia package manager. The online documentation, including examples, can be accessed at https://smoqysuite.github.io/SmoQyDEAC.jl/stable/.

Codebase release r1.1 for SmoQyDEAC.jl

We introduce the SmoQyDEAC.jl package, a Julia implementation of the Differential Evolution Analytic Continuation (DEAC) algorithm [N. S. Nichols et al., Phys. Rev. E 106, 025312 (2022)] for analytically continuing noisy imaginary time correlation functions to the real frequency axis. Our implementation supports fermionic and bosonic correlation functions on either the imaginary time or Matsubara frequency axes, and treatment of the covariance error in the input data. This paper presents an overview of the DEAC algorithm and the features implemented in the SmoQyDEAC.jl package. It also provides detailed benchmarks of the package’s output against the popular maximum entropy and stochastic analytic continuation methods. The code for this package can be downloaded from our GitHub repository at https://github.com/SmoQySuite/SmoQyDEAC.jl or installed using the Julia package manager. The online documentation, including examples, can be accessed at https://smoqysuite.github.io/SmoQyDEAC.jl/stable/.

An extended variational method for the resistive wall mode in toroidal plasma confinement devices

The external-kink stability of a toroidal plasma surrounded by a rigid resistive wall is investigated. The well-known analysis of Haney and Freidberg is rigorously extended to allow for a wall that is sufficiently thick that the thin-shell approximation does not necessarily hold. A generalized Haney–Freidberg formula for the growth-rate of the resistive wall mode is obtained. Thick-wall effects do not change the marginal stability point of the mode but introduce an interesting asymmetry between growing and decaying modes. Growing modes have growth-rates that exceed those predicted by the original Haney–Freidberg formula. On the other hand, decaying modes have decay-rates that are less than those predicted by the original formula. The well-known Hu–Betti formula for the rotational stabilization of the resistive wall mode is also generalized to take thick-wall effects into account. Increasing wall thickness facilitates the rotational stabilization of the mode, because it decreases the critical toroidal electromagnetic torque that the wall must exert on the plasma. On the other hand, the real frequency of the mode at the marginal stability point increases with increasing wall thickness.

Prediction of fishbone linear instability in tokamaks with machine learning methods

Abstract A machine learning based surrogate model for fishbone linear instability in tokamaks is constructed. Hybrid simulations with the kinetic-magnetohydrodynamic (MHD) code M3D-K is used to generate the database of fishbone linear instability, through scanning the four key parameters which are thought to determine the fishbone physics. The four key parameters include (1) central total beta of both thermal plasma and fast ions, (2) the fast ion pressure fraction, (3) central value of safety factor q and (4) the radius of q = 1 surface. Four machine learning methods including linear regression, support vector machines (SVM) with linear kernel, SVM with nonlinear kernel and multilayer perceptron are used to predict the fishbone instability, growth rate and real frequency, mode structure respectively. Among the four methods, SVM with nonlinear kernel performs very well to predict the linear instability with accuracy ≈ 95%, growth rate and real frequency with R2 ≈ 98%, mode structure with R2 ≈ 98%.

Investigating the Inharmonicity of Piano Strings

In classical physics, ideal string vibrations are modelled using the harmonic series, yet real mode frequencies deviate from the integer set of harmonics due to string stiffness, known as inharmonicity. This work investigates this phenomenon in five piano strings on a Yamaha GB1 Grand Piano. Using the audio software Audacity for spectral analysis, the inharmonicity coefficient is determined experimentally and theoretically based on string properties. These values are comparable with previous research, offering insights into tuning techniques to minimise dissonant inharmonicity. Possible innovations from inharmonicity research are explored, with suggestions such as the temperature-dependent self-tuning systems for acoustic pianos.

Role of nonthermal solar wind protons in the excitation of electromagnetic proton-cyclotron instability: a kinetic theory based exact numerical investigation

Free transverse kinetic energy i.e. perpendicular temperature anisotropy of protons excite the electromagnetic ion/proton cyclotron instability which is pertained to waves associated with prevalent electromagnetic ion/proton cyclotron emissions in various natural regions of plasmas. The transverse dielectric response function of left hand circularly polarized electromagnetic proton cyclotron (EPC) instability is calculated for two models of nonthermal Cairns distributed plasmas. These models are distinguished according to the effective thermal velocities of protons. For the energetic nonthermal protons populations, nonthermality dependent effective temperature model is proposed which significantly contributes in the excitation of aforementioned plasma mode and cause an appreciable enhancement in the instability growth rate. Exact numerical solution of dispersion relation yields oscillatory real frequency and growth rate of instability. A comparative analysis is also carried out to examine the instability behavior in distinct nonthermal and thermal plasma models. Contemporary numerical investigations are highly beneficial to understand the intricate dynamics of space plasmas.

Nevanlinna analytic continuation for Migdal–Eliashberg theory

In this work, we present a method to reconstruct real-frequency properties from analytically continued causal Green’s functions within the framework of Migdal–Eliashberg (ME) theory for superconductivity. ME theory involves solving a set of coupled equations self-consistently in imaginary frequency space, but to obtain experimentally measurable properties like the spectral function and quasiparticle density of states, it is necessary to perform an analytic continuation to real frequency space. Traditionally, the ME Green’s function is decomposed into three fundamental complex functions, which are analytically continued independently. However, these functions do not possess the causal properties of Green’s functions, complicating or even preventing the application of standard methods such as Maximum Entropy. Our approach overcomes these challenges, enabling the use of various analytic continuation techniques that were previously impractical. We demonstrate the effectiveness of this method by combining it with Nevanlinna analytic continuation to achieve accurate real-frequency results for ME theory, which are directly comparable to experimental data, with applications highlighted for the superconductors MgB2 and LaBeH8.

Direct Identification of the Continuous Relaxation Time and Frequency Spectra of Viscoelastic Materials

Relaxation time and frequency spectra are not directly available by measurement. To determine them, an ill-posed inverse problem must be solved based on relaxation stress or oscillatory shear relaxation data. Therefore, the quality of spectra models has only been assessed indirectly by examining the fit of the experiment data to the relaxation modulus or dynamic moduli models. As the measures of data fitting, the mean sum of the moduli square errors were usually used, the minimization of which was an essential step of the identification algorithms. The aim of this paper was to determine a relaxation spectrum model that best approximates the real unknown spectrum in a direct manner. It was assumed that discrete-time noise-corrupted measurements of a relaxation modulus obtained in the stress relaxation experiment are available for identification. A modified relaxation frequency spectrum was defined as a quotient of the real relaxation spectrum and relaxation frequency and expanded into a series of linearly independent exponential functions that are known to constitute a basis of the space of square-integrable functions. The spectrum model, given by a finite series of these basis functions, was assumed. An integral-square error between the real unknown modified spectrum and the spectrum model was taken as a measure of the model quality. This index was proved to be expressed in terms of the measurable relaxation modulus at uniquely defined sampling instants. Next, an empirical identification index was introduced in which the values of the real relaxation modulus are replaced by their noisy measurements. The identification consists of determining the spectrum model that minimizes this empirical index. Tikhonov regularization was applied to guarantee model smoothness and noise robustness. A simple analytical formula was derived to calculate the optimal model parameters and expressed in terms of the singular value decomposition. A complete identification algorithm was developed. The analysis of the model smoothness and model accuracy for noisy measurements was carried out. The equivalence of the direct identification of the relaxation frequency and time spectra has been demonstrated when the time spectrum is modeled by a series of functions given by the product of the relaxation frequency and its exponential function. The direct identification concept can be applied to both viscoelastic fluids and solids; however, some limitations to its applicability have been pointed out. Numerical studies have shown that the proposed identification algorithm can be successfully used to identify Gaussian-like and Kohlrausch–Williams–Watt relaxation spectra. The applicability of this approach to determining other commonly used classes of relaxation spectra was also examined.

Addressing the non-perturbative regime of the quantum anharmonic oscillator by physics-informed neural networks

Abstract The use of deep learning in physical sciences has recently boosted the ability of researchers to tackle physical systems where little or no analytical insight is available. Recently, the Physics−Informed Neural Networks (PINNs) have been introduced as one of the most promising tools to solve systems of differential equations guided by some physically grounded constraints. In the quantum realm, such an approach paves the way to a novel approach to solve the Schrödinger equation for non-integrable systems. By following an unsupervised learning approach, we apply the PINNs to the anharmonic oscillator in which an interaction term proportional to the fourth power of the position coordinate is present. We compute the eigenenergies and the corresponding eigenfunctions while varying the weight of the quartic interaction. We bridge our solutions to the regime where both the perturbative and the strong coupling theory work, including the pure quartic oscillator. We investigate systems with real and imaginary frequency, laying the foundation for novel numerical methods to tackle problems emerging in quantum field theory.

Effects of nonthermality on dust-acoustic surface waves with dust rotation

Abstract Dust Acoustic Surface Waves (DASWs) real frequency and group velocity are investigated for semi-bounded dusty plasma whose electrons and ions are modeled by Cairn s Distribution Function (CDF) while massive particles i.e. dust are treated Maxwellian. Kinetic approach based on Vlasov-Poisson s set of equations is used for the derivation of plasma dispersion relation. It is observed that in the presence of rotational parameter r and the variation of nonthermal index α affect both real frequency and group velocity of the wave significantly. This study has wide astrophysical applications.

Experimental probe of point gap topology from non-Hermitian Fermi-arcs

The gap in spectra of a physical system is fundamental in physics, while gap topology further restricts possible occurrent gaps of topological boundary states. The emergence of non-Hermiticity unveils a unique gap type known as the point gap, which forecasts the wavefunction localization, known as the non-Hermitian skin effect. Therefore, experimentally identifying the point gap in the complex frequency plane through a real operating frequency can become a tool for the systematic investigation of skin effects. Here, we utilize a Weyl phononic crystal to demonstrate that the point gap constituted by bulk and Fermi-arc surface states can be observed experimentally by a real-space field mapping technique. The identified point gaps forecast various skin effects and their evolutions. We further experimentally demonstrate the hinge skin effect in a parallelogram structure. Our work provides a feasible recipe to explore point gap topology experimentally in a variety of systems and certainly stimulates the research on skin effects in three-dimensional systems.

Quasinormal Frequencies of Fields with Various Spin in the Quantum Oppenheimer–Snyder Model of Black Holes

AbstractA recent development involves an intriguing model of a quantum‐corrected black hole, established through the application of the quantum Oppenheimer–Snyder model within loop quantum cosmology [Lewandowski et al., Phys. Rev. Lett. (2023) 130, 101501]. Employing both time‐domain integration and the Wentzel–Kramers–Brillouin (WKB) approach, the quasinormal frequencies for scalar, electromagnetic, and neutrino perturbations in these quantum‐corrected black holes are computed. This analysis reveals that while the real oscillation frequencies undergo only minor adjustments due to the quantum parameter, the damping rate experiences a significant decrease as a result of its influence. The author also deduced the analytic formula for quasinormal frequencies in the eikonal limit and showed that the correspondence between the null geodesics and eikonal quasinormal modes holds in this case.

Magnetic shaping effects on turbulence in ADITYA-U tokamak

The work reported in this paper addresses two aspects. In the first part, numerical simulations are conducted to examine the impact of magnetic equilibrium shaping (elongation and triangularity), on both conventional Ion Temperature Gradient (ITG) modes and Short Wavelength ITG modes. This analysis is performed considering the experimental profiles and parameters of the ADITYA-U tokamak, employing the nonlinear global gyrokinetic Particle-in-Cell code ORB5. The linear and nonlinear collisionless electrostatic simulation of these modes are carried out with kinetic ions and adiabatic electrons. From the linear results, it has been observed that the magnetic equilibrium shaping slighty reduced the growth rates and widened the spectrum, and the maxima of growth rate curve is shifted to higher toroidal wave number. We find that the heat flux is reduced by a significant ≃35% for the true circular magnetohydrodynamic magnetic equilibrium as compared to ad hoc concentric circular equilibrium reported in Singh et al (2023 Nucl. Fusion 63 086029). A further ≃10% reduction in the heat flux is seen with magnetic equilibrium shaping. In the second part, linear collisionless electrostatic simulation studies of ITG coupled with fully kinetic electrons (both trapped and passing electrons are treated kinetically) using a drift-kinetic ordering is performed. It can be seen from the linear results that, in presence of kinetic electrons, the growth rate and real frequency of the ITG mode are increased significantly for ADITYA-U parameters and a mode propagating in the electron diamagnetic direction is identified at high toroidal wavenumbers.

3.3-4.3 GHz efficient continuous class-F gallium nitride power amplifier based on simplified real frequency technique and harmonic tuning.

In order to implement the fifth generation (5G) communication system for a large number of users, the governments of many countries nominated the low 5G frequency band between 3.3 and 4.3 GHz. This paper proposes a wideband RFPA by designing the input matching network (MN) and output MN of the device using the simplified real frequency technique (SRFT) and the harmonic tuning network. The load-pull and source-pull is applied at multiple points for 100 MHz intervals over the bandwidth to obtain the optimum impedances at the output and input of the 10W Gallium Nitride (GaN) Cree CGH40010F device. To verify the design, the RFPA is simulated, and the performance is measured between 3.3 and 4.3 GHz. According to experimental findings, the measured drain efficiency (DE) throughout the whole bandwidth ranged from 57.5 to 67.5% at the output power of 40 dBm. Moreover, at the 1 dB compression point between 39.2 and 42.2 dBm output power, the drain efficiency (DE) achieves a high value of 81.2% with an output power of 42.2 dBm at a frequency of 3.3 GHz. The RFPA can obtain a maximum gain of 12.4 dB at 3.5 GHz. The linearity of the RFPA with a two-tone signal is measured and the value is less than -22 dBc all over the band.

KeldyshQFT: A C++ codebase for real-frequency multiloop functional renormalization group and parquet computations of the single-impurity Anderson model.

We provide a detailed exposition of our computational framework designed for the accurate calculation of real-frequency dynamical correlation functions of the single-impurity Anderson model in the regime of weak to intermediate coupling. Using quantum field theory within the Keldysh formalism to directly access the self-energy and dynamical susceptibilities in real frequencies, as detailed in our recent publication [Ge et al., Phys. Rev. B 109, 115128 (2024)], the primary computational challenge is the full three-dimensional real-frequency dependence of the four-point vertex. Our codebase provides a fully MPI+OpenMP parallelized implementation of the functional renormalization group (fRG) and the self-consistent parquet equations within the parquet approximation. It leverages vectorization to handle the additional complexity imposed by the Keldysh formalism, using optimized data structures and highly performant integration routines. Going beyond the results shown in the previous publication, the code includes functionality to perform fRG calculations in the multiloop framework, up to arbitrary loop order, including self-consistent self-energy iterations. Moreover, implementations of various regulators, such as hybridization, interaction, frequency, and temperature, are supplied.

Real time implementation of downlink orthogonal frequency division multiplexing based non-orthogonal multiple access transceiver using NI USRP platform

The growing fame and utilization of wireless multimedia approaches have led to the advancement of the wireless system. The fifth generation (5G) of wireless communication was developed to serve users with enhanced proficiency, low latency, reliable communication, and lesser battery exhausts. The non-orthogonal multiple access (NOMA) scheme is a proficient multiple access scheme to fulfil the requirement of a 5G mobile system. NOMA enables a remarkable enhancement in the systems throughput and ability to connect devices. NOMA distinguishes each user by allocating a distinct power level, superimposing all the user’s signals utilizing superposition coding while transmitting and at the reception, each user’s signals are decoded by employing successive interference cancellation (SIC). This study builds a real time downlink orthogonal frequency division multiplexing based NOMA (OFDM-NOMA) transceiver system using the NI USRP 2944R and 2901 platforms. The performance evaluation of the proposed OFDM-NOMA system is carried out in terms of signal to noise ratio by adjusting transmitting gain and the distance of users from the base station system. Experimental results show that the signal-to-noise ratio (SNR) of each user relies on the power allocation factor and proximity of users from the base station, and SIC output is compared with constellation variations.

Ab Initio Study of the Graphyne-like γ-SiC Nanoflake for Toxic Gas-Sensing Applications.

This study focuses on the geometrical, electronic, and optical properties of the γ-graphyne-like novel γ-SiC nanoflake of the γ-silicon carbide (SiC) monolayer using density functional theory calculations. γ-SiC was revealed to be a stable semiconducting nanoflake confirmed by a negative cohesive energy, real vibrational frequencies, and a 1.749 eV energy gap. The adsorption of COCl2, HCN, PH3, AsH3, CNCl, and C2N2 toxic gases on the γ-SiC nanoflake is also studied, which revealed an attractive gas-nanoflake interaction with the adsorption energy ranging from -0.21 to -0.38 eV. The adsorption results in a significant charge transfer between gas-adsorbent complexes. A significant variation in the energy gap and electrical conductivity was observed due to gas adsorption. γ-SiC showed maximum sensitivity at room temperature for CNCl gas. The entire process of adsorption is exothermic and thermodynamically stable. γ-SiC showed a high absorption coefficient over 104 orders with a significant variation in the absorption peak intensity and blue peak shifting. According to the quantum theory and reduced density gradient analysis, all of the gases are physisorbed on the γ-SiC nanoflake due to van der Waals interactions. The obtained results signify the usability of γ-SiC as a potential toxic gas sensor.

Design of dual-band power amplifier based on microstrip coupled-line bandstop filter

This article presents a simple and effective method for designing a dual-band power amplifier (PA). A microstrip coupled-line bandstop filter (BSF) is cascaded with a broadband PA, thus a notched band can be obtained in the wide operating band, realizing a dual-band characteristic of the PA. The simplified real frequency technique (SRFT) is employed to derive a broadband input matching networks covering the requisite frequency band. Appropriate fundamental impedance and second harmonic impedance matching are achieved at the ideal region of the Smith chart. For validation, an experimental prototype is fabricated and tested using a commercial GaN transistor Cree’s CGH40010F. The proposed dual-band PA is operated at 1.95–2.4 GHz and 2.65–3.1 GHz, with 61%–71% measured power-added efficiency (PAE) and 40.5–41.5 dBm of measured output power.

Fault prioritisation for Air Handling units using fault modelling and actual fault occurrence data

Fault impact analysis is an important step in developing Fault Detection and Diagnosis (FDD) tools for Heating, Ventilation and Air-Conditioning (HVAC) systems. It provides an insight into how HVAC systems react in the presence of operational faults and helps to prioritise which faults to focus on. The research in the existing literature has mostly focused on modelling several faults occurring in various HVAC systems and components to evaluate the effect of the fault on energy performance and the predicted thermal comfort of occupants. However, the real frequency of fault occurrence, an important factor which affects the overall impact a fault has on the system’s performance, has barely been addressed in the reviewed literature. This paper addresses this gap by considering real fault occurrence frequency data in addition to the effect of the faults on the energy performance of the building to assess their total energy impact. A real office building in the Netherlands was modelled using DesignBuilder and its energy performance was simulated using EnergyPlus. Air Handling Unit (AHU) faults were introduced using the native fault object and Energy Management System (EMS) features available in EnergyPlus. The fault occurrence data was extracted from AHU work orders using text mining. The fault modelling and text mining results were combined to get the total energy impact of the fault and, subsequently, the faults were prioritised using the Pareto principle. The research identified that fan failure, Heat Recovery Wheel (HRW) failure, fan stuck at 50% and Heating Coil Valve (HCV) stuck at 0% are the priority faults for winter and fan failure is the priority fault for summer.

ECONOMIC AND MATHEMATICAL MODELING OF THE RENEWABLE ENERGY DEVELOPMENT IN UKRAINE

Objective. The objective of the article is to apply economic and mathematical models for the analysis, modeling and forecasting of the development of renewable energy in Ukraine, assessment of country's renewable energy sources potential. Methods. The following methods are used to model and forecast the development of renewable energy in Ukraine: correlational and actocorrelational analysis (to identify the relationship between macroeconomic indicators of Ukraine and the development of renewable energy in the country); three-factor autoregressive and multiplicative forecasting and five-factor regression forecasting (for forecasting indicators of renewable energy of Ukraine); the basics of the mathematical apparatus for the analysis of transient processes, the methodology of determining the coefficients of impulse-transient and transient functions, methods of building differential models, Laplace transformation and obtaining transient functions, the basics of the mathematics of imaginary quantities, methods of obtaining the amplitude-phase and frequency characteristics of the object under study, methods of analysis stability of controlled dynamic processes (to present the Total renewable energy indicator in the form of a dynamic transient process and model its future states by obtaining a second-order differential equation with a simple input, a complex transfer function and by determining the amplitude-phase frequency characteristic and constructing a Nyquist frequency hodograph, which showed the stability of the studied process to external disturbances). Results. Forecasting the installed capacities and production volumes of renewable energy is an important task for the effective development of this industry. A new approach to forecasting is proposed, combining autoregressive and multivariate regression models and dynamic modeling. The development of the capacity of renewable energy is considered as a dynamic transient process, which is represented by a complex transfer function with its real frequency characteristic and its imaginary frequency characteristic, which are used to construct the Nyquist hodograph, which shows the stability of the researched process of development of the capacity of renewable energy from investment investments. According to the results of modeling based on the transient process method, a model of changes in the volume of installed capacities of renewable energy of Ukraine depending on the volume of investments in renewable energy is obtained in the form of a differential equation, and it is found out that this process is stable, that is, even with temporary restrictions or reductions of such investment over time it will return to a stable growing trend. The proposed method of dynamic modeling makes it possible to obtain more accurate and reliable forecasts of the development of renewable energy capacity, compared to traditional methods. This method can be used to make informed decisions regarding the development of solar energy and investment in this industry in Ukraine.