Isogeometric analysis for functionally graded microplates based on modified couple stress theory

Analysis of static bending, free vibration and buckling behaviours of functionally graded microplates is investigated in this study. The main idea is to use the isogeometric analysis in associated with novel four-variable refined plate theory and quasi-3D theory. More importantly, the modified couple stress theory with only one material length scale parameter is employed to effectively capture the size-dependent effects within the microplates. Meanwhile, the quasi-3D theory which is constructed from a novel seventh-order shear deformation refined plate theory with four unknowns is able to consider both shear deformations and thickness stretching effect without requiring shear correction factors. The NURBS-based isogeometric analysis is integrated to exactly describe the geometry and approximately calculate the unknown fields with higher-order derivative and continuity requirements. The convergence and verification show the validity and efficiency of this proposed computational approach in comparison with those existing in the literature. It is further applied to study the static bending, free vibration and buckling responses of rectangular and circular functionally graded microplates with various types of boundary conditions. A number of investigations are also conducted to illustrate the effects of the material length scale, material index, and length-to-thickness ratios on the responses of the microplates.Comment: 57 pages, 14 figures, 18 table

Perspectives for a mixed two-qubit system with binomial quantum states

The problem of the relationship between entanglement and two-qubit systems in which it is embedded is central to the quantum information theory. This paper suggests that the concurrence hierarchy as an entanglement measure provides an alternative view of how to think about this problem. We consider mixed states of two qubits and obtain an exact solution of the time-dependent master equation that describes the evolution of two two-level qubits (or atoms) within a perfect cavity for the case of multiphoton transition. We consider the situation for which the field may start from a binomial state. Employing this solution, the significant features of the entanglement when a second qubit is weakly coupled to the field and becomes entangled with the first qubit, is investigated. We also describe the response of the atomic system as it varies between the Rabi oscillations and the collapse-revival mode and investigate the atomic inversion and the Q-function. We identify and numerically demonstrate the region of parameters where significantly large entanglement can be obtained. Most interestingly, it is shown that features of the entanglement is influenced significantly when the multi-photon process is involved. Finally, we obtain illustrative examples of some novel aspects of this system and show how the off-resonant case can sensitize entanglement to the role of initial state setting.Comment: 18 pages, 9 figure

Design of thermally deformable laminates using machine learning

Recent advances in material science and manufacturing have enabled designers to create objects which respond to changing environmental conditions by controlled deformation, without external mechanical or electrical actuation. The design of such smart materials has mostly been done through trial and error due to their complex nonlinear behavior. This paper will present how this problem is addressed by introducing a novel inverse design workflow. In this, a desired structural deformation is used as an input to a machine learned model which subsequently outputs the required geometric and material properties that will produce said deformation when exposed to an external stimulus. This workflow uses a Generative Adversarial Neural Network (GANN) trained on pairs of input cut-out patterns of laminate layers and their nonlinear Finite Element Analysis (FEA) simulation results. The method offers a significant performance speed-up while maintaining acceptable levels of accuracy, especially at the early design stage. This methodology could be further extended to the design of any nonlinear mechanical deformation

Kappa-deformed random-matrix theory based on Kaniadakis statistics

We present a possible extension of the random-matrix theory, which is widely used to describe spectral fluctuations of chaotic systems. By considering the Kaniadakis non-Gaussian statistics, characterized by the index {\kappa} (Boltzmann-Gibbs entropy is recovered in the limit {\kappa}\rightarrow0), we propose the non-Gaussian deformations ({\kappa} \neq 0) of the conventional orthogonal and unitary ensembles of random matrices. The joint eigenvalue distributions for the {\kappa}-deformed ensembles are derived by applying the principle maximum entropy to Kaniadakis entropy. The resulting distribution functions are base invarient as they depend on the matrix elements in a trace form. Using these expressions, we introduce a new generalized form of the Wigner surmise valid for nearly-chaotic mixed systems, where a basis-independent description is still expected to hold. We motivate the necessity of such generalization by the need to describe the transition of the spacing distribution from chaos to order, at least in the initial stage. We show several examples about the use of the generalized Wigner surmise to the analysis of the results of a number of previous experiments and numerical experiments. Our results suggest the entropic index {\kappa} as a measure for deviation from the state of chaos. We also introduce a {\kappa}-deformed Porter-Thomas distribution of transition intensities, which fits the experimental data for mixed systems better than the commonly-used gamma-distribution.Comment: 18 pages, 8 figure

On the SigmaN cusp in the pp -> pK+Lambda reaction

Measurements of the $pp \to pK^+\Lambda$ reaction at $T_p$ = 2.28 GeV have been carried out at COSY-TOF. In addition to the $\Lambda p$ FSI and $N^*$ resonance excitation effects a pronounced narrow structure is observed in the Dalitz plot and in its projection on the $p\Lambda$-invariant mass. The structure appears at the $pp \to$N$K^+\Sigma$ threshold and is interpreted as $\Sigma$N cusp effect. The observed width of 20 MeV/$c^2$ is substantially broader than anticipated from previous inclusive measurements. Angular distributions of this cusp structure are shown to be dissimilar to those in the residual $pK^+\Lambda$ channel, but similar to those observed in the $pK^+\Sigma^0$ channel

Correlation between TcT_c and anisotropic scattering in Tl2_2Ba2_2CuO6+δ_{6+\delta}

Angle-dependent magnetoresistance measurements are used to determine the isotropic and anisotropic components of the transport scattering rate in overdoped Tl$_2$Ba$_2$CuO$_{6+\delta}$ for a range of $T_c$ values between 15K and 35K. The size of the anisotropic scattering term is found to scale linearly with $T_c$, establishing a link between the superconducting and normal state physics. Comparison with results from angle resolved photoemission spectroscopy indicates that the transport and quasiparticle lifetimes are distinct.Comment: 5 pages, 3 figures, accepted for publication in Physical Review Letter

Systematic study of the pp -> pp omega reaction

A systematic study of the production of omega-mesons in proton-proton-collisions was carried out in a kinematically complete experiment at three excess energies(epsilon= 92, 128, 173MeV). Both protons were detected using the large-acceptance COSY-TOF spectrometer at an external beam line at the Cooler Synchrotron COSY at Forschungszentrum J\"ulich. The total cross section, angular distributions of both omega-mesons and protons were measured and presented in various reference frames such as the overall CMS, helicity and Jackson frame. In addition, the orientation of the omega-spin and invariant mass spectra were determined. We observe omega-production to take place dominantly in Ss and Sp final states at epsilon = 92, 128 MeV and, additionally, in Sd at epsilon= 173 MeV. No obvious indication of resonant omega-production via N^*-resonances was found, as proton angular distributions are almost isotropic and invariant mass spectra are compatible with phase space distributions. A dominant role of ^3P_1 and ^1S_0 initial partial waves for omega-production was concluded from the orientation of the decay plane of the omega-meson. Although the Jackson angle distributions in the omega-p-Jackson frame are anisotropic we argue that this is not an indication of a resonance but rather a kinematical effect reflecting the anisotropy of the omega angular distribution. The helicity angle distribution in the omega-p-helicity frame shows an anisotropy which probably reflects effects of the omega angular momenta in the final state; this observable may be, in addition to the orientation of the omega decay plane, the most sensitive one to judge the validity of theoretical descriptions of the production process.Comment: 17 pages, 16 figures, accepted for publication in EPJ

Flat Cosmology with Coupled Matter and Dark Energies

Three models of a flat universe of coupled matter and dark energies with different low-redshift parameterizations of the dark energy equation of state are considered. The dark energy is assumed to vary with time like the trace of the energy-momentum tensor of cosmic matter. In the radiation-dominated era the models reduce to standard cosmology. In the matter-dominated era they are, for modern values of the cosmological parameters, consistent with data from SNe Ia searches and with the data of Gurvits et al.(1999)for angular sizes of ultra compact radio sources. We find that the angular size-redshift tests for our models offer a higher statistical confidence than that based on SNe Ia data. A comparison of our results with a recent revised analysis of angular size-redshift legacy data is made,and the implications of our models with optimized relativistic beaming in the radio sources is discussed. In particular we find that relativistic beaming implies a Lorentz factor less than 6,in agreement with its values for powerful Active Galactic Nuclei.Comment: Version to appear in The Astronomical Journal, with a modified name- Flat Cosmology with Coupled Matter and Dark Energies. Expanded and Modified conten