Linear Fluctuations Research Articles

Investigation of wind load characteristics of cantilevered scaffolding of a high-rise building based on field measurement

Over recent years, rigid porous plates with higher wind resistance coefficients have become more frequent in construction projects, replacing flexible dense mesh safety nets. This change has resulted in a substantial increase in the load on the surface of the clad scaffolding. The paper is centered on the characteristics of wind load on the cantilever construction scaffolding of a high-rise building in Xi’an, with the objective of concluding the distribution rules by field measurement. The study revealed that the non-Gaussian characteristics of wind pressure are most pronounced near the incoming separation point and the middle of the building surface. The local wind force coefficient adheres to a logarithmic distribution pattern with the wind pressure turbulence. The turbulence, gust factor, and skewness and kurtosis of fluctuating wind pressure exhibit an “S-like” distribution along the building surface. Based on the research findings, as the wind pressure increases significantly, two correlations between the mean value of the fluctuating stress and fluctuating wind pressure were identified: linear and mean fluctuation.

Growth of and Fluctuations in India’s GDP and GDP Accruing from Agriculture During 1970-71 to 2019-20

In India, agricultural sector output plays a significant role in the beginning phase of the growth of the economy because it absorbs the majority of employment. The agriculture sector includes crop production, livestock rearing, forestry, and fishing. However, the agricultural sector has experienced several fluctuations due to various factors, such as monsoon variability, natural disasters, government policies, and market conditions. These fluctuations have had a substantial influence on the overall economic growth of the nation. In this present paper, we try to find the linear growth and fluctuations around the linear of India's GDP and the agricultural sector output for 50 years long period from 1970-71 to 2019-20. The outcome of this study reveals that the annual average growth rate is 5.52% for GDP and 2.89% for the agricultural sector. The Coppock based year-to-year fluctuation around the trend is 0.00089 for gross domestic product and 0.00191 for the agricultural sector output. The overall fluctuation using the RSS-based method is 0.00520 for GDP and 0.00309 for GDPA.

ANALYSIS OF THE POSSIBILITIES OF MODERN RESEARCH METHODS FOR THE DIAGNOSTIC OF HEMORRAGE IN THE SUBSTANCE OF THE HUMAN BRAIN (LITERATURE REVIEW)

Traumatic brain injury is one of the most widespread and complex types of mechanical injury today, which involves many fields of medical practice, including neurosurgery, neurology, rehabilitation, forensic medicine, etc., and requires a multidisciplinary approach to its solution. Aim of the work: to analyse, on the basis of data from literary sources, the possibilities of modern research methods for the diagnosis of haemorrhages in the substance of the human brain and their genesis. Research results. The gold standard for verification of the diagnosis in forensic medicine is a forensic histological examination, however, the classical technique of histological differential diagnosis of the genesis and time of formation of a haemorrhage in the brain substance is not effective. The diagnosis of traumatic brain injury can be complicated in cases where there are no macroscopic signs of head trauma and little information is available about the circumstances of death. Therefore, a number of researchers have explored the possibility of using biomarkers to provide objective evidence of traumatic brain injury as the cause of death or to estimate the survival and post-mortem time of the deceased. Biophysical studies using a laser have shown potential success in the field of traumatic brain injury diagnostics. Preliminary conclusions regarding the possibility of differentiating the genesis of cerebral haemorrhage using the method of reconstructing distributions of the magnitude of linear dichroism fluctuations gave positive results. Conclusion. It was found that biochemical studies show significant success in the diagnosis of traumatic brain injury, some markers even make it possible to differentiate the genesis of brain haemorrhage, but forensic medical practice requires the development of easy-to-use, highly effective methods to verify the type of human brain injury. This role can potentially be fulfilled by physical-optical methods based on laser irradiation of biological objects followed by mathematical and statistical processing of the obtained data.

Quantum decoherence dynamics in stochastically fluctuating environments.

We theoretically study the decoherence of a two-level quantum system coupled to noisy environments exhibiting linear and quadratic fluctuations within the framework of a stochastic Liouville equation. It is shown that the intrinsic energy levels of the quantum system renormalize under either the linear or quadratic influence of the environmental noise. In the case of quadratic dependence, the renormalization of the energy levels of the system emerges even if the environmental noise exhibits stationary statistical properties. This is in contrast to the case under linear influence, where the intrinsic energy levels of the system renormalize only if the environmental noise displays nonstationary statistics. We derive the analytical expressions of the decoherence function in the cases where the fluctuation of the frequency difference depends linearly and quadratically on the nonstationary Ornstein-Uhlenbeck noise (OUN) and random telegraph noise (RTN) processes, respectively. In the case of the linear dependence of the OUN, the environmental nonstationary statistical property can enhance the dynamical decoherence. However, the nonstationary statistics of the environmental noise can suppress the quantum decoherence in this case under the quadratic influence of the OUN. In the presence of the RTN, the quadratic influence of the environmental noise does not give rise to decoherence but only causes a determinate frequency renormalization in dynamical evolution. The environmental nonstationary statistical property can suppress the quantum decoherence of the case under the linear influence of the RTN.

Exploring Long-Term Persistence in Sea Surface Temperature and Ocean Parameters via Detrended Cross-Correlation Approach

Long-term cross-correlational structures are examined for pairs of sea surface temperature anomalies (SSTAs) and advective forcing parameters and sea surface height anomalies (SSHAs) and current velocity anomalies (CVAs) in the East/Japan Sea (EJS); all these satellite datasets were collected between 1993 and 2023. By utilizing newly modified detrended cross-correlation analysis algorithms, incorporating local linear trend and local fluctuation level of an SSTA, the analyses were performed on timescales of 400–3000 days. Long-term cross-correlations between SSTAs and SSHAs are strongly persistent over nearly the entire EJS; the strength of persistence is stronger during rising trends and low fluctuations of SSTAs, while anti-persistent behavior appears during high fluctuations of SSTAs. SSTA-CVA pairs show high long-term persistence only along main current pathways: the zonal currents for the Subpolar Front and the meridional currents for the east coast of Korea. SSTA-CVA pairs also show negative long-term persistent behaviors in some spots located near the coasts of Korea and Japan: the zonal currents for the eastern coast of Korea and the meridional currents for the western coast of Japan; these behaviors seem to be related to the coastal upwelling phenomena. Further, these persistent characteristics are more conspicuous in the recent decades (2008~2023) rather than in the past (1993~2008).

Feedback linearization control to avoid saturation of the high frequency transformer of a dual active bridge DC–DC converter for a DC microgrid

This paper introduces an innovative control strategy for a dual active bridges DC–DC converter employed to regulate voltage levels between two feeders in a DC microgrid. The controller is specifically designed to regulate the output voltage at a predetermined reference value and to ensure a zero mean value for both primary and secondary currents of the high-frequency transformer, regardless of any imbalance in one of the active bridges. This is particularly important in the face of potential imbalances in one of the active bridges resulting from construction disparities in converters or variations in conduction resistances in power transistors. Given the nonlinear nature of the converter, the controller is designed using feedback linearization. The output is selected with a relative degree equal to the system order, resulting in a stable controller exhibiting good dynamic performance under scenarios such as reference changes, linear load fluctuations, and the integration of constant power loads. The performance of the proposed control strategy is validated through both simulation and experimental results.

The effects of non-linearity on the growth rate constraint from velocity correlation functions

ABSTRACT The two-point statistics of the cosmic velocity field, measured from galaxy peculiar velocity (PV) surveys, can be used as a dynamical probe to constrain the growth rate of large-scale structures in the Universe. Most works use the statistics on scales down to a few tens of Megaparsecs, while using a theoretical template based on the linear theory. In addition, while the cosmic velocity is volume-weighted, the observable line-of-sight velocity two-point correlation is density-weighted, as sampled by galaxies, and therefore the density–velocity correlation term also contributes, which has often been neglected. These effects are fourth order in powers of the linear density fluctuation $\delta _{\rm L}^4$, compared to $\delta _{\rm L}^2$ of the linear velocity correlation function, and have the opposite sign. We present these terms up to $\delta _{\rm L}^4$ in real space based on the standard perturbation theory, and investigate the effect of non-linearity and the density–velocity contribution on the inferred growth rate fσ8, using N-body simulations. We find that for a next-generation PV survey of volume $\sim {\cal O}(500 \, h^{-1} \, {\rm Mpc})^3$, these effects amount to a shift of fσ8 by ∼10 per cent and is comparable to the forecasted statistical error when the minimum scale used for parameter estimation is $r_{\rm min} = 20 \, h^{-1} \, {\rm Mpc}$.

Forecasting Post-Epidemic Air Passenger Flow Among Hub Cities in China Based on PLS and GA-SVR Model

For stakeholders and companies involved in civil aviation to plan and make wise decisions, accurate estimates of air passenger flow are necessary. The conclusions drawn from this model serve as an invaluable resource for pertinent choices. The top hub cities in mainland China's air travel network are predicted using a variable weight combination model that combines PLS and GA-SVR. According to the test results, the model developed in this study improves prediction accuracy. This demonstrates how well detailed information about social and economic development can be gleaned from linear development patterns and nonlinear fluctuation rules. Predictions can be made with more accuracy and a better fit as a result. Over the next five years, it is predicted that over 300 million passengers will fly between the top hub cities in mainland China, an increase of 6.51% per year. The growth in passenger traffic varies significantly between different routes. The routes from Beijing to Shanghai and Shanghai to Shenzhen saw the most travellers, while the Beijing-Chengdu route saw the fastest growth in traveller numbers. The study's findings provide useful advice for civil aviation businesses and people involved in their decision-making, fostering growth in the sector during the post-pandemic period.

New tool for 21-cm cosmology. II. Investigating the effect of early linear fluctuations

New tool for 21-cm cosmology. II. Investigating the effect of early linear fluctuations

The Hopf whole-brain model and its linear approximation

Whole-brain models have proven to be useful to understand the emergence of collective activity among neural populations or brain regions. These models combine connectivity matrices, or connectomes, with local node dynamics, noise, and, eventually, transmission delays. Multiple choices for the local dynamics have been proposed. Among them, nonlinear oscillators corresponding to a supercritical Hopf bifurcation have been used to link brain connectivity and collective phase and amplitude dynamics in different brain states. Here, we studied the linear fluctuations of this model to estimate its stationary statistics, i.e., the instantaneous and lagged covariances and the power spectral densities. This linear approximation—that holds in the case of heterogeneous parameters and time-delays—allows analytical estimation of the statistics and it can be used for fast parameter explorations to study changes in brain state, changes in brain activity due to alterations in structural connectivity, and modulations of parameter due to non-equilibrium dynamics.

Nonlinear dynamics of fractional viscoelastic PET membranes with linearly varying density

In this paper, the nonlinear dynamics of fractional viscoelastic polyethylene terephthalate (PET) membranes with linearly varying density are elaborated. The viscoelasticities of the PET membranes are characterized with the fractional Kelvin–Voigt model, and the density distribution is considered a linear fluctuation in the lateral direction. The geometrically nonlinear formulation is established with the von-Karman theory and the Hamilton principle. The Bubnov–Galerkin method is used to solve the resulting fractional differential equations, and a refined numerical scheme combining the finite difference with a discrete Caputo-type fractional derivative approximation is developed. Comparison examples are provided to substantiate the accuracy and effectiveness of the present method. A detailed parametric analysis is performed to illuminate the effects of the fractional order, density coefficient and various system parameters on the time response of the viscoelastic PET membranes. This study paves the way for fractional modelling and vibrational analysis of viscoelastic substrates in flexible electronics manufacturing.

Gravity and matter on a pure geometric thick polynomial f(R) brane

In this paper, the solutions of the pure geometric thick $f(R)$ brane are investigated. The formulation of $f(R)$ is chosen as $f(R)=\sum_{i=1}^{n}a_{i}R^{i}+\Lambda$. For the certain value of $n$, the brane solution can be calculated, and when $n=3$, $n=4$, and $n=10$, the thick brane solutions are presented. The solutions is stable under linear tensor fluctuation. The zero mode of gravity and scalar field can be localized on thick $f(R)$ branes naturally. The zero mode of vector field and left-chiral fermion can be localized on thick $f(R)$ branes by introducing the coupling with scalar curvature $R$ of spacetime, and the massive resonant modes can be quasilocalized on the brane with the large coupling coefficients.

Wide-angle and relativistic effects in Fourier-space clustering statistics

Galaxy power spectrum and bispectrum signals are distorted by peculiar velocities and other relativistic effects arising from a perturbed spacetime background. In addition, study of correlation functions of tracers in Fourier space is often done in the plane-parallel approximation under which it is assumed that line-of-sight (LOS) vectors are parallel. In this work we show that a simple perturbative procedure can be employed for a fast evaluation of beyond plane-parallel (wide-angle) corrections to the power spectrum and bispectrum. We also show that evolution of linear matter density fluctuations in a relativistic context can be found from a simple method. For the power spectrum at linear level, we compare leading order wide-angle contributions to multipoles of the galaxy power spectrum with those from non-integrated and integrated relativistic corrections and estimate their possible contamination on local fNL measurements to be of order a few. We also compute wide-angle corrections in the presence of nonlinear terms at one-loop order. For the bispectrum, we show that wide-angle effects alone, even with fully symmetric choices of LOS, give rise to imaginary, odd-parity multipoles of the galaxy bispectrum (dipole, octupole, etc.) which are in many cases larger than previously known ones of relativistic origin. We calculate these contributions and provide an estimator for measuring the leading order bispectrum dipole from data, using a symmetric LOS definition. Finally, we calculate the leading order corrections to multipoles of real plane-parallel bispectrum multipoles and estimate the apparent local fNL induced to be of order unity.

Mass renormalization in lattice simulations of false vacuum decay

False vacuum decay, a quantum mechanical first-order phase transition in scalar field theories, is an important phenomenon in early Universe cosmology. Recently, real-time semiclassical techniques based on ensembles of lattice simulations were applied to the problem of false vacuum decay. In this context, or any other lattice simulation, the effective potential experienced by long-wavelength modes is not the same as the bare potential. To make quantitative predictions using the real-time semiclassical techniques, it is therefore necessary to understand the redefinition of model parameters and the corresponding deformation of the vacuum state, as well as stochastic contributions that require modeling of unresolved subgrid modes. In this work, we focus on the former corrections and compute the expected modification of the true and false vacuum effective mass, which manifests as a modified dispersion relationship for linear fluctuations about the vacuum. We compare these theoretical predictions to numerical simulations and find excellent agreement. Motivated by this, we use the effective masses to fix the shape of a parametrized effective potential, and explore the modeling uncertainty associated with nonlinear corrections. We compute the decay rates in both the Euclidean and real-time formalisms, finding qualitative agreement in the dependence on the UV cutoff. These calculations further demonstrate that a quantitative understanding of the rates requires additional corrections.

Time Domain Investigation of Hybrid Intelligent Controllers Fed Five-Phase PMBLDC Motor Drive

This paper presents a modeling and performance evaluation of a five-phase PMBLDC motor with different controllers to analyze its transients and dynamic response with time domain specifications. Four different types of speed controllers, namely an Adaptive Neuro-Fuzzy Inference System (ANFIS), an Adaptive Hybrid fuzzy-PI, a Proportional Integral (PI) control and a Fuzzy Logic Control (FLC), were considered and compared for this purpose. The mathematical model of the five-phase Permanent Magnet Brushless Direct Current (PMBLDC) motor was developed and simulated using MATLAB/Simulink to analyze its performance. The simulation results for all controllers with step and linear load fluctuations were evaluated. It was evident that the ANFIS controller provided a better dynamic time domain response than the other controllers. It gave eight times the peak torque at starting, and settled at 92.6% of the rated speed, with negligible overshoot, a very low rise time and a quick settling time compared to other controllers, which are ideally suited for an electric vehicle (EV). A real-time experimental setup was also developed, and experiments were carried out to validate the simulation results.

Variable Switching Frequency Deadbeat Predictive Current Control for PMSM with High-Speed and Low-Carrier Ratio

The predictive current control method of permanent magnet synchronous motor has the advantages of fast dynamic response and easy digital implementation, so more attention has been paid to it. When the motor operates in a high-speed condition, the switching frequency is relatively low, the carrier ratio is low, and the rotor angle varies greatly within a control cycle, resulting in a large error in the traditional liner approximation prediction model and inaccuracy of the voltage control quantity calculation, which leads to the deterioration of the predictive current control effect. At the same time, the output harmonic of the three-phase current increases, which affects the stable operation of the motor. In this paper, we study the causes of the large errors in the prediction model based on the traditional linear approximation and phase current fluctuation of the permanent magnet synchronous motor under high speed and low carrier-ratio conditions. Based on the improvement of the prediction model and modulation, a new control strategy of variable switching frequency deadbeat predictive current control is proposed. The control method proposed in this paper improves the dynamic and steady-state performance of the motor, under the condition that the carrier ratio does not increase and reduces the fluctuation of the output current of the motor. Finally, the effectiveness and superiority of the proposed method are verified by an experiment.

Extended primordial black hole mass functions with a spike

ABSTRACT We introduce a modification of the Press–Schechter formalism aimed to derive general mass functions for primordial black holes (PBHs). In this case, we start from primordial power spectra (PPS) which include a monochromatic spike, typical of ultra slow-roll inflation models. We consider the PBH formation as being associated to the amplitude of the spike on top of the linear energy density fluctuations coming from a PPS with a blue index. By modelling the spike with a lognormal function, we study the properties of the resulting mass function spikes, and compare these to the underlying extended mass distributions. When the spike is at PBH masses, which are much lower than the exponential cut-off of the extended distribution, very little mass density is held by the PBHs within the spike, and it is not ideal to apply the Press–Schechter formalism in this case as the resulting characteristic overdensity is too different from the threshold for collapse. It is more appropriate to do so when the spike mass is similar to, or larger than the cut-off mass. Additionally, it can hold a similar mass density as the extended part. Such particular mass functions also contain large numbers of small PBHs, especially if stable PBH relics are considered, and they can provide ${\sim}1000\, {\rm M}_\odot$ seeds for the supermassive black holes at the centres of present-day galaxies. The constraints on the fraction of dark matter in PBHs for monochromatic mass functions are somewhat relaxed when there is an additional underlying extended distribution of masses.

Linearized off-shell 4+7 supergeometry of 11D supergravity

We describe the linearized supergeometry of eleven dimensional supergravity with four off-shell local supersymmetries. We start with a background Minkowski 11D, N=1 superspace, and an additional ingredient of a global, constant, G2-structure which facilitates the definition of a 4|4 + 7 background superspace. A bottom-up construction of linear fluctuations of the geometric constituents (such as supervielbein, spin connection, and the super 3-form of 11D supergravity) is given in terms of 4D, N=1 prepotential superfields. This is complemented by a top-down description of the linearized supergeometry of the 4|4 + 7 superspace dealing directly with torsion, curvature, and Bianchi identities. Torsion constraints that (combined with the Bianchi identities) lead to the preceding prepotential expressions of the gauge fields are identified. All irreducible consequences of the torsion and 4-form Bianchi identities are systematically derived except for dimension 2 Bianchi identities of the 4-form, and dimension frac{5}{2} Bianchi identities of torsion, which set bosonic curls of components of one lower dimension to zero.

Birefringence and dichroism effects in the spin noise spectra of a spin-1 system

We perform spin noise spectroscopy experiments in metastable helium atoms at room temperature, with a probe light whose frequency is blue detuned from the D 0 line. Both circular birefringence fluctuations (Faraday noise) and linear birefringence fluctuations (ellipticity noise) are explored theoretically and experimentally. In particular, it is shown that in both cases but for different optical detunings, two noise resonances are isolated at the Larmor frequency and at twice the Larmor frequency with a behavior, which strongly depends on the orientation of the probe field polarization. The simple structure of metastable helium allows us to probe, model and explain the changes in the behavior of these peaks in terms of circular and linear dichroisms and birefringences as well as in terms of spin oscillation modes.

A stable and causal model of magnetohydrodynamics

We formulate the theory of first-order dissipative magnetohydrodynamics in an arbitrary hydrodynamic frame under the assumption of parity-invariance and discrete charge symmetry. We study the mode spectrum of Alfvén and magnetosonic waves as well as the spectrum of gapped excitations and derive constraints on the transport coefficients such that generic equilibrium states with constant magnetic fields are stable and causal under linearised perturbations. We solve these constraints for a specific equation of state and show that there exists a large family of hydrodynamic frames that renders the linear fluctuations stable and causal. This theory does not require introducing new dynamical degrees of freedom and therefore is a promising and simpler alternative to Müller-Israel-Stewart-type theories. Together with a detailed analysis of transport, entropy production and Kubo formulae, the theory presented here is well suited for studying dissipative effects in various contexts ranging from heavy-ion collisions to astrophysics.