Identification of the Fractional Zener Model Parameters for a Viscoelastic Material over a Wide Range of Frequencies and Temperatures

The paper presents an analysis of the rheological properties of a selected viscoelastic material, which is dedicated to the reduction of vibrations in structures subjected to dynamic loads. A four-parameter, fractional Zener model was used to describe the dynamic behavior of the tested material. The model parameters were identified on the basis of laboratory tests performed at different temperatures and for different vibration frequencies. After proving that the material is thermoreologically simple, the so-called master curves were created using a horizontal shift factor. The Williams–Landel–Ferry formula was applied to create graphs of the master curves, the constants of which were determined for the selected temperature. The resulting storage and loss module functions spanned several decades in the frequency domain. The parameters of the fractional Zener model were identified by fitting the entire range of the master curves with the gradientless method (i.e., Particle Swarm Optimization), consisting in searching for the best-fitted solution in a set of feasible solutions. The parametric analysis of the obtained solutions allowed for the formulation of conclusions regarding the effectiveness of the applied rheological model.

Testing and Modelling of Elastomeric Element for an Embedded Rail System

Modelling of elastomeric elements of railway components, able to represent stiffness and damping characteristics in a wide frequency range, is fundamental for simulating the train–track dynamic interaction, covering issues such as rail deflection as well as transmitted forces and higher frequency phenomena such as short pitch corrugation. In this paper, a modified non-linear Zener model is adopted to represent the dependences of stiffness and damping of the rail fastening, made of elastomeric material, of a reference Embedded Rail System (ERS) on the static preload and frequency of its deformation. In order to obtain a reliable model, a proper laboratory test set-up is built, considering sensitivity and frequency response issues. The equivalent stiffness and damping of the elastomeric element are experimentally characterised with force-controlled mono-harmonic tests at different frequencies and under various static preloads. The parameters of the non-linear Zener model are identified by the experimental equivalent stiffness and damping. The identified model correctly reproduces the frequency- and preload-dependent dynamic properties of the elastomeric material. The model is verified to be able to predict the dynamic behaviour of the elastomeric element through the comparison between the numerically simulated and the experimentally measured reaction force to a given deformation time history. Time domain simulations with the model of the reference ERS demonstrate that the modelled frequency- and preload-dependent stiffness and damping of the elastomeric material make a clear difference in the transient and steady-state response of the system when distant frequency contributions are involved.

Nonadiabatic nonlinear optics and quantum geometry — Application to the twisted Schwinger effect

We study the tunneling mechanism of nonlinear optical processes in solids induced by strong coherent laser fields. The theory is based on an extension of the Landau-Zener model with nonadiabatic geometric effects. In addition to the rectification effect known previously, we find two effects, namely perfect tunneling and counterdiabaticity at fast sweep speed. We apply this theory to the twisted Schwinger effect, i.e., nonadiabatic pair production of particles by rotating electric fields, and find a nonperturbative generation mechanism of the opto-valley polarization and photo-current in Dirac and Weyl fermions.

Adiabatic critical quantum metrology cannot reach the Heisenberg limit even when shortcuts to adiabaticity are applied

We show that the quantum Fisher information attained in an adiabatic approach to critical quantum metrology cannot lead to the Heisenberg limit of precision and therefore regular quantum metrology under optimal settings is always superior. Furthermore, we argue that even though shortcuts to adiabaticity can arbitrarily decrease the time of preparing critical ground states, they cannot be used to achieve or overcome the Heisenberg limit for quantum parameter estimation in adiabatic critical quantum metrology. As case studies, we explore the application of counter-diabatic driving to the Landau-Zener model and the quantum Rabi model.

Transient vibrations of a fractional Zener viscoelastic cantilever beam with a tip mass

The presented work concerns the kinematically excited transient vibrations of a cantilever beam with a mass element fixed to its free end. The Euler–Bernoulli beam theory and the fractional Zener model of the beam material are assumed. A fractional Caputo derivative is used to formulate a viscoelastic material law. A characteristic equation, modal frequencies, eigenfunction and orthogonality conditions are achieved for the beam considered. The equations of motion of the system are solved numerically. A numerical solution of a multi-term fractional differential equation is obtained by means of a conversion to a mixed system of ordinary and fractional differential equations, each of the order of $$0 < \gamma \le 1$$ 0 < γ ≤ 1 . The transient time histories of the beam vibrations during the passage through resonance are calculated. A comparison between the beam responses obtained with a fractional and an integer viscoelastic material model is presented. The calculations performed reveal that use of the fractional damping affects on the time histories of the system. The calculated beam responses show that for some values of the order of the fractional derivative $$\gamma$$ γ , the amplitudes occurring in the area of the second resonance are greater than those obtained in the area of the first resonance, which does not occur in the case of the integer order of the fractional derivative. Moreover, an evaluation is made of the difference between the results obtained for the calculations using the fractional Zener model and the fractional Kelvin model. It is shown that for some physical beam parameters, the calculation results obtained using both models are virtually the same for both models, which means that the the simpler, fractional Kelvin–Voigt material can be used instead of the fractional Zener material model. This simplifies the solution and decreases the time needed to make the numerical calculations.

Simultaneous Characterization of Relaxation, Creep, Dissipation, and Hysteresis by Fractional-Order Constitutive Models

We considered relaxation, creep, dissipation, and hysteresis resulting from a six-parameter fractional constitutive model and its particular cases. The storage modulus, loss modulus, and loss factor, as well as their characteristics based on the thermodynamic requirements, were investigated. It was proved that for the fractional Maxwell model, the storage modulus increases monotonically, while the loss modulus has symmetrical peaks for its curve against the logarithmic scale log(ω), and for the fractional Zener model, the storage modulus monotonically increases while the loss modulus and the loss factor have symmetrical peaks for their curves against the logarithmic scale log(ω). The peak values and corresponding stationary points were analytically given. The relaxation modulus and the creep compliance for the six-parameter fractional constitutive model were given in terms of the Mittag–Leffler functions. Finally, the stress–strain hysteresis loops were simulated by making use of the derived creep compliance for the fractional Zener model. These results show that the fractional constitutive models could characterize the relaxation, creep, dissipation, and hysteresis phenomena of viscoelastic bodies, and fractional orders α and β could be used to model real-world physical properties well.

The exact WKB for cosmological particle production

The Bogoliubov transformation in cosmological particle production can be explained by the Stokes phenomena of the corresponding ordinary differential equation. The calculation becomes very simple as far as the solution is described by a special function. Otherwise, the calculation requires more tactics, where the Exact WKB (EWKB) may be a powerful tool. Using the EWKB, we discuss cosmological particle production focusing on the effect of more general interaction and classical scattering. The classical scattering appears when the corresponding scattering problem of the Schrödinger equation develops classical turning points on the trajectory. The higher process of fermionic preheating is also discussed using the Landau-Zener model.