Dynamic Stability Analysis of Size-Dependent Viscoelastic/Piezoelectric Nano-beam

This paper analyzes the dynamic stability of an isotropic viscoelastic Euler–Bernoulli nano-beam using piezoelectric materials. For this purpose, the size-dependent theory was used in the framework of the modified couple stress theory (MCST) for piezoelectric materials. In order to capture the geometrical nonlinearity, the von Karman strain displacement relation was applied. Hamilton’s principle was also employed to obtain the governing equations. Furthermore, the Galerkin method was used in order to convert the governing partial differential equations (PDEs) to a nonlinear second-order ordinary differential one. Dynamic stability analysis was performed and the effects of such parameters as viscoelastic coefficients, size effect, and piezoelectric coefficient were investigated. The results showed that in this system, saddle points, central points, Hopf bifurcation points, and fork bifurcation points could be created, and the phase portraits connecting these equilibrium points exhibit periodic orbits, heteroclinic orbits, and homoclinic orbits.

Bouncing with shear: implications from quantum cosmology

We consider the introduction of anisotropy in a class of bouncing models of cosmology. The presence of anisotropy often spells doom on bouncing models, since the energy density due to the anisotropic stress outweighs that of other matter components, as the universe contracts. Different suggestions have been made in the literature to resolve this pathology, classically. Here, we introduce a family of bouncing models, in which the shear density can be tuned to either allow or forbid classical bouncing scenarios. Following which, we show that quantum cosmological considerations can drastically change the above scenario. Most importantly, we find that quantum effects can enable a bounce, even when the anisotropic stress is large enough to forbid the same classically. We employ the solutions of the appropriate mini-superspace Wheeler-deWitt equation for homogeneous, but anisotropic cosmologies, with the boundary condition that the universe is initially contracting. Intriguingly, the solution to the Wheeler-deWitt equation exhibit an interesting phase transition-like behaviour, wherein, the probability to have a bouncing universe is precisely unity before the shear density reaches a critical value and then starts to decrease abruptly as the shear density increases further. We verified our findings using the tools of the Lorentzian quantum cosmology, along with the application of the Picard-Lefschetz theory. In particular, the semi-classical probability for bounce has been re-derived from the imaginary component of the on-shell effective action, evaluated at the complex saddle points. Implications and future directions have also been discussed.

RALR: Random Amplify Learning Rates for Training Neural Networks

It has been shown that the learning rate is one of the most critical hyper-parameters for the overall performance of deep neural networks. In this paper, we propose a new method for setting the global learning rate, named random amplify learning rates (RALR), to improve the performance of any optimizer in training deep neural networks. Instead of monotonically decreasing the learning rate, we expect to escape saddle points or local minima by amplifying the learning rate between reasonable boundary values based on a given probability. Training with RALR rather than conventionally decreasing the learning rate achieves further improvement on networks’ performance without extra consumption. Remarkably, the RALR is complementary with state-of-the-art data augmentation and regularization methods. Besides, we empirically study its performance on image classification tasks, fine-grained classification tasks, object detection tasks, and machine translation tasks. Experiments demonstrate that RALR can bring a notable improvement while preventing overfitting when training deep neural networks. For example, the classification accuracy of ResNet-110 trained on the CIFAR-100 dataset using RALR achieves a 1.34% gain compared with ResNet-110 trained traditionally.

The Whale Optimization Algorithm Approach for Deep Neural Networks

One of the biggest challenge in the field of deep learning is the parameter selection and optimization process. In recent years different algorithms have been proposed including bio-inspired solutions to solve this problem, however, there are many challenges including local minima, saddle points, and vanishing gradients. In this paper, we introduce the Whale Optimisation Algorithm (WOA) based on the swarm foraging behavior of humpback whales to optimise neural network hyperparameters. We wish to stress that to the best of our knowledge this is the first attempt that uses Whale Optimisation Algorithm for the optimisation task of hyperparameters. After a detailed description of the WOA algorithm we formulate and explain the application in deep learning, present the implementation, and compare the proposed algorithm with other well-known algorithms including widely used Grid and Random Search methods. Additionally, we have implemented a third dimension feature analysis to the original WOA algorithm to utilize 3D search space (3D-WOA). Simulations show that the proposed algorithm can be successfully used for hyperparameters optimization, achieving accuracy of 89.85% and 80.60% for Fashion MNIST and Reuters datasets, respectively.

Transition pathways connecting crystals and quasicrystals

Due to structural incommensurability, the emergence of a quasicrystal from a crystalline phase represents a challenge to computational physics. Here, the nucleation of quasicrystals is investigated by using an efficient computational method applied to a Landau free-energy functional. Specifically, transition pathways connecting different local minima of the Lifshitz–Petrich model are obtained by using the high-index saddle dynamics. Saddle points on these paths are identified as the critical nuclei of the 6-fold crystals and 12-fold quasicrystals. The results reveal that phase transitions between the crystalline and quasicrystalline phases could follow two possible pathways, corresponding to a one-stage phase transition and a two-stage phase transition involving a metastable lamellar quasicrystalline state, respectively.

Magneto-optic signatures in the gapped Dirac semimetal with mixed linear and parabolic dispersions of ZrTe5

In this paper, we give a systematic theoretical study on the Landau levels (LLs) and magneto-optical conductivity Re(σαα) in a gapped Dirac semimetal model with mixed linear and parabolic dispersions under a magnetic field, which was recently proposed by Jiang et al. [Phys. Rev. Lett. 125, 046403 (2020)] to explain the experimental magnetoinfrared spectroscopy in the three-dimensional ZrTe5 crystal. We find that the strong magnetic field can drive the LLs become noninverted and thus the strong topological insulator phase in ZrTe5 turns to be a trivial insulator. In the different magnetic field regions, the density of states and Re(σαα) can exhibit distinct signatures. Moreover, when the magnetic field is weak, a qualitative relation in Re(σzz) between the peaks at the saddle points is revealed as Re(σzz ζn) >Re(σzz Γ) , which is in good agreement with the experiment.

Absolute instability in shock-containing jets

We present an analysis of the linear stability characteristics of shock-containing jets. The flow is linearised around a spatially periodic mean, which acts as a surrogate for a mean flow with a shock-cell structure, leading to a set of partial differential equations with periodic coefficients in space. Disturbances are written using the Floquet ansatz and Fourier modes in the streamwise direction, leading to an eigenvalue problem for the Floquet exponent. The characteristics of the solution are directly compared with the locally parallel case, and some of the features are similar. The inclusion of periodicity induces minor changes in the growth rate and phase velocity of the relevant modes for small shock amplitudes. On the other hand, the eigenfunctions are now subject to modulation related to the periodicity of the flow. Analysis of the spatio-temporal growth rates led to the identification of a saddle point between the Kelvin–Helmholtz mode and the guided jet mode, characterising an absolute instability mechanism. Frequencies and mode shapes related to the saddle points for two conditions (associated with axisymmetric and helical modes) are compared with screech frequencies and the most energetic coherent structures of screeching jets, resulting in a good agreement for both. The analysis shows that a periodic shock-cell structure has an impulse response that grows upstream, leading to oscillator behaviour. The results suggest that screech can occur in the absence of a nozzle, and that the upstream reflection condition is not essential for screech frequency selection. Connections to previous models are also discussed.

Phase profile of the wave function of canonical tensor model and emergence of large space–times

In this paper, to understand space–time dynamics in the canonical tensor model of quantum gravity for the positive cosmological constant case, we analytically and numerically study the phase profile of its exact wave function in a coordinate representation, instead of the momentum representation analyzed so far. A saddle point analysis shows that Lie group symmetric space–times are strongly favored due to abundance of continuously existing saddle points, giving an emergent fluid picture. The phase profile suggests that spatial sizes grow in “time,” where sizes are measured by the tensor-geometry correspondence previously introduced using tensor rank decomposition. Monte Carlo simulations are also performed for a few small N cases by applying a re-weighting procedure to an oscillatory integral which expresses the wave function. The results agree well with the saddle point analysis, but the phase profile is subject to disturbances in a large space–time region, suggesting existence of light modes there and motivating future computations of primordial fluctuations from the perspective of canonical tensor model.

Experimental PIV investigation of the PZT fans array coupling effect at high Reynolds numbers

Piezoelectric fan arrays are being increasingly emphasized for heat dissipation in small-sized electronic devices. In this study, PIV experiments were conducted to investigate the flow fields induced by piezoelectric fan arrays with different vibration modes and pitches at high Reynolds numbers (324< Re <509) in a stationary air environment. As a result, when the PZT fan array is vibrating in-phase, the saddle points in the time averaged flow field are formed and separated gradually as the pitch increases, the remnant vortex and the induced vortex interact to form a jet with a periodic oscillation in the direction. Jet velocity reaches a maximum at P = 3A. In counter-phase vibration, saddle points are separated from one region under large pitches, the interaction of counter-rotating induced vortices forms a vertical upward jet. The morphology of induced and remnant vortices with different vibration modes and array pitches are responsible for the jet formation and flow field pattern. The interaction of counter-rotating vortices in counter-phase vibration leads the jet intensity higher than in-phase vibration induced jet, the optimal setting of the PZT fan under this study is determined as P = 2.5A with counter-phase vibration. The experimental results provide validation for the simulation study and give guidance to the application