Late time transition of Universe and the hybrid scale factor

In this study, we propose an interacting model to explain the physical mechanism of the late time transition from matter-dominated era to the dark energy-dominated era of the Universe evolution and to obtain a scale factor a(t) representing two eras together. In the present model, we consider a minimal coupling of two scalar fields which correspond to the dark matter and dark energy interacting through a potential based on the FLRW framework. Analytical solution of this model leads to a new scale factor a(t) in the hybrid form $$a(t)=a_{0} (t/t_{0})^{\alpha } e^{ht/t_{0}}$$ a ( t ) = a 0 ( t / t 0 ) α e h t / t 0 . This peculiar result reveals that the scale factor behaving as $$a (t) \propto (t/t_{0})^{\alpha }$$ a ( t ) ∝ ( t / t 0 ) α in the range $$t/t_{0}\le t_{c}$$ t / t 0 ≤ t c corresponds to the matter-dominated era while $$a(t) \propto \exp (ht/t_{0})$$ a ( t ) ∝ exp ( h t / t 0 ) in the range $$t/t_{0}>t_{c}$$ t / t 0 > t c accounts for the dark energy-dominated era, respectively. Surprisingly, we explore that the transition from the power-law to the exponential expansion appears at the crossover time $$t_{0} \approx 9.8$$ t 0 ≈ 9.8 Gyear. We attain that the presented model leads to precisely correct results so that the crossover time $$t_{0}$$ t 0 and $$\alpha $$ α are completely consistent with the exact solution of the FLRW and re-scaled Hubble parameter $$H_{0}$$ H 0 lies within the observed limits given by Planck, CMB and SNIa data (or other combinations), which lead to consistent cosmological quantities such as the dimensionless Hubble parameter h, deceleration parameter q, jerk parameter j and EoS parameter w. We also discuss time dependent behavior of the dark energy and dark matter to show their roles on the time evolution of the universe. Additionally, we observe that all main results completely depend on the structure of the interaction potential when the parameter values are tuned to satisfy the zero energy condition. Finally, we conclude that interactions in the dark sector may play an important role on the time evolution and provides a mechanism to explain the late time transition of the Universe.

Calibration Method of Accelerometer Based on Rotation Principle Using Double Turntable Centrifuge

For linear accelerometers, calibration with a precision centrifuge is a key technology, and the input acceleration imposed on the accelerometer should be accurately obtained in the calibration. However, there are often errors in the installation of sample that make the calibration inaccurate. To solve installation errors and obtain the input acceleration in the calibration of the accelerometer, a calibration method based on the rotation principle using a double turntable centrifuge is proposed in this work. The key operation is that the sub-turntable is rotated to make the input axis of the accelerometer perpendicular to the direction of the centripetal acceleration vector. Models of installation errors of angle and radius were built. Based on these models, the static radius and input acceleration can be obtained accurately, and the calibration of the scale factor, nonlinearity and asymmetry can be implemented. Using this method, measurements of the MEMS accelerometer with a range of ±30 g were carried out. The results show that the discrepancy of performance obtained from different installation positions was smaller than 100 ppm after calibrating the input acceleration. Moreover, the results using this method were consistent with those using the back-calculation method. These results demonstrate that the effectiveness of our proposed method was confirmed. This method can measure the static radius directly eliminating the installation errors of angle and radius, and it simplifies the accelerometer calibration procedure.

Structural Design and Optimization of a Resonant Micro-Accelerometer Based on Electrostatic Stiffness by an Improved Differential Evolution Algorithm

This study designed an in-plane resonant micro-accelerometer based on electrostatic stiffness. The accelerometer adopts a one-piece proof mass structure; two double-folded beam resonators are symmetrically distributed inside the proof mass, and only one displacement is introduced under the action of acceleration, which reduces the influence of processing errors on the performance of the accelerometer. The two resonators form a differential structure that can diminish the impact of common-mode errors. This accelerometer realizes the separation of the introduction of electrostatic stiffness and the detection of resonant frequency, which is conducive to the decoupling of accelerometer signals. An improved differential evolution algorithm was developed to optimize the scale factor of the accelerometer. Through the final elimination principle, excellent individuals are preserved, and the most suitable parameters are allocated to the surviving individuals to stimulate the offspring to find the globally optimal ability. The algorithm not only maintains the global optimality but also reduces the computational complexity of the algorithm and deterministically realizes the optimization of the accelerometer scale factor. The electrostatic stiffness resonant micro-accelerometer was fabricated by deep dry silicon-on-glass (DDSOG) technology. The unloaded resonant frequency of the accelerometer resonant beam was between 24 and 26 kHz, and the scale factor of the packaged accelerometer was between 54 and 59 Hz/g. The average error between the optimization result and the actual scale factor was 7.03%. The experimental results verified the rationality of the structural design.

The role of scale factor in the formation of prod-uct properties under the action of surface modifi-cation

Based on theoretical and experimental research in the fields of solid-state physics and physical materials science, it is proved that the surface layer of a solid body, which is deformed, is an independent functional subsystem and radically affects large-scale levels of plastic flow and destruction of the product as a whole. As is known, the most effective method of improving the performance of products is the grinding of grain, because it is the grain boundary (substructural) mechanism of strengthening which provides an increase in the structural strength of the product. In this regard, special attention is paid to submicro- and nano-structuring of the surface. Goal. The aim of the work is to study the process of structure formation of the surface layer under the action of ion bombardment (IB) and its effect on the properties of products taking into account the scale factor. To achieve this goal, the following tasks were set: to evaluate the characteristics of the surface microstructure after IB and to study its tensile behavior in cylindrical and flat samples of low-carbon steel in order to take into account the scale factor in changing their properties. The submicro-structuring of the surface by ion bombardment is carried out in the work and its influence on the behavior of products during tensile deformation is investigated. It is established that the presence of a thin modified layer (with a constant core) significantly changes the properties of the product under force. The decisive role belongs to the contribution of the surface layer (scale factor) – the ratio of the area of the modified layer to the volume of the product: if it is <1 the effect of hardening is better realized while maintaining plasticity, and if ˃ 1, it is a significant effect of plasticization which maintains (or even increases) hardening.

Lorentzian quantum cosmology goes simplicial

We employ the methods of discrete (Lorentzian) Regge calculus for analysing Lorentzian quantum cosmology models with a special focus on discrete analogues of the no-boundary proposal for the early universe. We use a simple 4-polytope, a subdivided 4-polytope and shells of discrete 3-spheres as triangulations to model a closed universe with cosmological constant, and examine the semiclassical path integral for these different choices. We find that the shells give good agreement with continuum results for small values of the scale factor and in particular for finer discretisations of the boundary 3-sphere, while the simple and subdivided 4-polytopes can only be compared with the continuum in certain regimes, and in particular are not able to capture a transition from Euclidean geometry with small scale factor to a large Lorentzian one. Finally, we consider a closed universe filled with dust particles and discretised by shells of 3-spheres. This model can approximate the continuum case quite well. Our results embed the no-boundary proposal in a discrete setting where it is possibly more naturally defined, and prepare for its discussion within the realm of spin foams.

Levy walk dynamics in non-static media

Almost all the media the particles move in are non-static, one of which is the most common expanding or contracting (by a scale factor) non-static medium discussed in this paper. Depending on the expected resolution of the studied dynamics and the amplitude of the displacement caused by the non-static media, sometimes the non-static behaviors of the media can not be ignored. In this paper, we build the model describing L\'evy walks in one-dimension uniformly non-static media, where the physical and comoving coordinates are connected by scale factor. We derive the equation governing the probability density function of the position of the particles in comoving coordinate. Using the Hermite orthogonal polynomial expansions, some statistical properties are obtained, such as mean squared displacements (MSDs) in both coordinates and kurtosis. For some representative non-static media and L\'{e}vy walks, the asymptotic behaviors of MSDs in both coordinates are analyzed in detail. The stationary distributions and mean first passage time for some cases are also discussed through numerical simulations.