Suppressing measurement uncertainty in an inhomogeneous spin star system

The uncertainty principle is known as a foundational element of quantum theory, providing a striking lower bound to quantify our prediction for the measured result of two incompatible observables. In this work, we study the thermal evolution of the entropic uncertainty bound in the presence of quantum memory for an inhomogeneous four-qubit spin-star system that is in the thermal regime. Intriguingly, our results show that the entropic uncertainty bound can be controlled and suppressed by adjusting the inhomogeneity parameter of the system.

Finite element method for stress and strain analysis of FGM hollow cylinder under effect of temperature profiles and inhomogeneity parameter

This study represents a numerical analysis of stress and strain in the functionally graded material (FGM) hollow cylinder subjected to two different temperature profiles and inhomogeneity parameter. The thermo-mechanical properties of a cylinder are assumed to vary continuously as power law function along the radial coordinate of a cylinder. Based on equilibrium equation, Hooke's law, stress-strain relationship in the cylinders, and other theories from mechanics second order differential equation is obtained that represents the thermoelastic field in hollow FGM cylinder. To find a numerical solution of governing differential equation, the finite element method (FEM) with standard discretization approach is used. The analysis of numerical results reveals that stress and strain in the FGM cylinder are significantly depend upon variation made in temperature profile and inhomogeneity parameter n. The results show good agreement with results available in the literature. It is shown that thermoelastic characteristics of the FGM cylinder are controlled by controlling the value of the above discussed parameters. Moreover, these results are very useful in various fields of engineering and science as FGM cylinders have a wide range of applications in these fields.

Thermally induced vibrations in an inhomogeneous fiber-reinforced thermoelastic medium with gravity

PurposeThe present investigation is concerned with the two-dimensional deformations in an inhomogeneous fiber-reinforced thermoelastic medium under the influence of gravity in the context of Green–Lindsay theory.Design/methodology/approachMaterial properties are supposed to be graded in x-direction, and normal mode technique is adopted to obtain the exact expressions for the temperature field, displacement components and stresses.FindingsNumerical computations have been carried out with the help of MATLAB software, and the results are depicted graphically to observe the disturbances induced in the considered medium. Comparisons made within the theory of the physical quantities are shown in figures to highlight the effects of fiber reinforcement, inhomogeneity parameter, gravity and time.Originality/valueIn the present work, we have investigated the effects of fiber reinforcement, inhomogeneity parameter, gravity and time in an inhomogeneous, fiber-reinforced thermoelastic medium under the influence of gravity. Although various investigations do exist to observe the disturbances in a thermoelastic medium under the effects of different parameters, the work in its present form i.e. thermally induced vibrations in an inhomogeneous fiber-reinforced thermoelastic material with gravity has not been studied till now. The present work is useful and valuable for analysis of problems involving thermal shock, gravity parameter, fiber reinforcement, inhomogeneous and elastic deformation.

Contact behavior of functionally graded fractal surface

Functionally graded surface has been a domain of research interest due to its use in various technologically advanced applications. The work focuses on static and dynamic analysis of rough fractal surface with exponentially graded material properties. The rough fractal surface is modeled in ANSYS with the coordinate points generated using the two variable modified Weierstrass–Mandelbrot function. Material gradation is applied to the rough surface model in such a way that, for any value of the gradation or inhomogeneity parameter, material properties at the top of the rough surface always remain constant. Force–displacement behavior of the fractal surface in contact with a rigid flat surface is determined through finite element simulation. A parameter representing the nonlinearity of the system is extracted from the force–displacement plot. It is found that higher is the inhomogeneity parameter, higher is the nonlinearity of the system. Furthermore, for a certain change in inhomogeneity parameter, the change in nonlinearity is higher for rougher topography. The dynamic contact system is found to be softening in nature, and the softening nature increases with higher inhomogeneity parameter. The phase plot of the vibrating contact system becomes more asymmetric with respect to the velocity axis for higher value of inhomogeneity parameter.

Modeling and Numerical Analysis in 3D of Anisotropic and Nonlinear Mechanical Behavior of Tournemire Argillite under High Temperatures and Dynamic Loading

This work proposes a model that takes into account the anisotropy of material with its inhomogeneity and geometrical and material nonlinearities. According to Newton’s second law, the investigations were carried out on the simultaneous effects of mechanical load and thermal treatment on the Tournemire argillite material. The finite difference method was used for the numerical resolution of the problem by the MATLAB 2015a software in order to determine the peak stress and strain of argillite as a function of material nonlinearity and demonstrated the inhomogeneity parameter Ω. The critical temperature from which the material damage was pronounced is 500°C. Indeed, above this temperature, the loss of rigidity of argillite reduced significantly the mechanical performance of this rock. Therefore, after 2.9 min, the stress reduction in X or Y direction was 75.5% with a peak stress value of 2500 MPa, whereas in Z direction, the stress reduction was 74.1% with a peak stress value of 1998 MPa. Meanwhile, knowing that the material inhomogeneity was between 2995 and 3256.010, there was an increase in peak stress of about 75%. However, the influence of the material nonlinearity was almost negligible. Thus, the geometrical nonlinearity allows having the maximal constant strain of about 1.25 in the direction of the applied dynamic mechanical force.

Shear wave propagation in magneto poroelastic medium sandwiched between self-reinforced poroelastic medium and poroelastic half space

Purpose The purpose of this paper is to investigate the effect of reinforcement, inhomogeneity and initial stress on the propagation of shear waves. The problem consists of magneto poroelastic medium sandwiched between self-reinforced medium and poroelastic half space. Using Biot’s theory of wave propagation, the frequency equation is obtained. Design/methodology/approach Shear wave propagation in magneto poroelastic medium embedded between a self-reinforced medium and poroelastic half space is investigated. This particular setup is quite possible in the Earth crust. All the three media are assumed to be inhomogeneous under initial stress. The significant effects of initial stress and inhomogeneity parameters of individual media have been studied. Findings Phase velocity is computed against wavenumber for various values of self-reinforcement, heterogeneity parameter and initial stress. Classical elasticity results are deduced as a particular case of the present study. Also in the absence of inhomogeneity and initial stress, frequency equation is discussed. Graphical representation is made to exhibit the results. Originality/value Shear wave propagation in magneto poroelastic medium embedded between a self-reinforced medium, and poroelastic half space are investigated in presence of initial stress, and inhomogeneity parameter. For heterogeneous poroelastic half space, the Whittaker’s solution is obtained. From the numerical results, it is observed that heterogeneity parameter, inhomogeneity parameter and reinforcement parameter have significant influences on the wave characteristics. In addition, frequency equation is discussed in absence of inhomogeneity and initial stress. For the validation purpose, numerical results are also computed for a particular case.

Seismic Q of inhomogeneous plane waves in porous media

Seismic waves in an attenuative porous medium are generally inhomogeneous waves, which have different directions of propagation and attenuation. The dissipation factors (1/ Q) of inhomogeneous waves are strongly dependent on the degree of wave inhomogeneity and cannot be expressed correctly with the usual 1/ Q expressions valid only for homogeneous waves. We have used the differing definitions of 1/ Q for inhomogeneous waves (i.e., the ratio of the time-averaged dissipated energy density to the time-averaged strain energy density or time-averaged total energy density) and the complex form of the energy balance equations of poroviscoelastic media to derive concise and explicit expressions for the dissipation factors. They are given as simple functions of the material parameters and the wave inhomogeneity parameter for inhomogeneous SV-waves and fast and slow P-waves. The isotropic, poroviscoelastic medium under consideration is upscaled from effective Biot theory for a double-porosity solid, which is the most general theory to describe wave propagation in a reservoir. We find that, if the inhomogeneity parameter is infinite (i.e., the inhomogeneity angle is 90°) for all three Biot waves, then the dissipation factors only depend on the ratio of the imaginary to the real part of the complex shear modulus. Our explicit expressions for the dissipation factors of poroviscoelastic materials also are reduced to obtain their counterparts for viscoelastic media as a special case. The inhomogeneous waves in an example poroviscoelastic material are used to demonstrate that the 1/ Q values of the three Biot waves strongly depend on the inhomogeneity parameters and furthermore the different definitions may cause significant differences of 1/ Q values. We find that the dissipation factor of fast P-waves may decrease with the increasing degree of inhomogeneity, which contradicts previously published results.

A new classification of satellite-derived liquid water cloud regimes at cloud scale

Clouds are highly variable in time and space, affecting climate sensitivity and climate change. To study and distinguish the different influences of clouds on the climate system, it is useful to separate clouds into individual cloud regimes. In this work we present a new cloud classification for liquid water clouds at cloud scale defined using cloud parameters retrieved from combined satellite measurements from CloudSat and CALIPSO. The idea is that cloud heterogeneity is a measure that allows us to distinguish cumuliform and stratiform clouds, and cloud-base height is a measure to distinguish cloud altitude. The approach makes use of a newly developed cloud-base height retrieval. Using three cloud-base height intervals and two intervals of cloud-top variability as an inhomogeneity parameter provides six new liquid cloud classes. The results show a smooth transition between marine and continental clouds as well as between stratiform and cumuliform clouds in different latitudes at the high spatial resolution of about 20 km. Analysing the micro- and macrophysical cloud parameters from collocated combined MODIS, CloudSat and CALIPSO retrievals shows distinct characteristics for each cloud regime that are in agreement with expectation and literature. This demonstrates the usefulness of the classification.

Explicit Q expressions for inhomogeneous P- and SV-waves in isotropic viscoelastic media

We derive explicit expressions for the dissipation factors of inhomogeneous P and SV-waves in isotropic viscoelastic media. The Q−1 values are given as concise and simple functions of material parameters and the wave inhomogeneity parameter using two different definitions. Unlike homogenous waves, inhomogeneous waves may have significant differences in the values of dissipation factors because of different definitions. For example, under one of the three dissipation factor definitions that Q−1 is equal to the time-averaged dissipated-energy density divided by twice the time-averaged strain-energy density, it is found and proved that the dissipation factor of SV-waves is totally independent of the inhomogeneity parameter. For materials in which P-waves are normally more dissipative than S-waves (e.g. a porous reservoir), the dissipation factors of P-waves tend to decrease with increasing degree of inhomogeneity. Based on Buchan's classic real value energy balance equation, a parallel investigation is conducted for each step similar to that based on the Carcione equations, including derivation of explicit formulas (with inhomogeneity angle representing the degree of inhomogeneity of a plane wave), and dissipation curves calculations. We also obtain an inhomogeneity independent formula of $Q_{\, SV}^{ - 1}$, and exactly the same phase velocity and attenuation dispersion results for the example material.

Thermal Buckling of Functionally Graded Sandwich Beams

Thermal buckling of new model of functionally graded (FG) sandwich beams is presented in this study. Material properties and thermal expansion coefficient of FG sheets are assumed to vary continuously along the thickness according to either power-law (P-FGM) or sigmoid function (S-FGM) in terms of the volume fractions of the constituents. Equations of stability are derived based on the generalized higher-order shear deformation beam theory. Thermal loads are supposed to be constant, linear or nonlinear distribution along the thickness direction. An accurate form solution for nonlinear temperature variation through the thickness of S-FGM and P-FGM sandwich beams is presented. Numerical examples are presented to examine the influence of thickness ratio, the inhomogeneity parameter and the thermal loading kinds on the thermal buckling response of various types of FG sandwich beams.