Quo Vadis Nonlinear Optics? An Alternative and Simple Approach to Third Rank Tensors in Semiconductors

It is well understood that nonlinear optical (NLO) phenomena are deeply related to the material’s symmetry. Mathematically, the material symmetry can be described in terms of the nonzero parameters in the nonlinear susceptibility tensors. Generally, more complex structures involve more nonzero parameters in the tensor. The number of parameters increases rapidly if higher NLO orders are considered, complicating the physical analysis. Conventionally, these parameters are obtained via abstract symmetry analysis, e.g., group theory (GT). This work presents a novel theoretical analysis to approach the nonlinear tensor using the simplified bond hyperpolarizability model (SBHM) and compare it with GT. Our analysis is based on a light–matter interaction classical phenomenological physical framework. Rather than just looking at the symmetry of the crystal, the model applies physical considerations requiring fewer independent parameters in the tensor than GT. Such a simplification significantly improves the determination of the surface–bulk SHG contribution factors, which cannot be extracted from the experiment alone. We also show for the case of perovskite that the SHG contribution can be addressed solely from their surface dipoles with only one independent component in the tensor. Therefore, this work may open the path for a similar analysis in other complicated semiconductor surfaces and structures in the future, with potential applications to nanoscale surface characterization and real-time surface deposition monitoring.

New Elements of Analysis of a Degenerate Chenciner Bifurcation

A new transformation of parameters for generic discrete-time dynamical systems with two independent parameters is defined, for when the degeneracy occurs. Here the classical transformation of parameters (α1,α2)→(β1,β2) is not longer regular at (0,0); therefore, implicit function theorem (IFT) cannot be applied around the origin, and a new transformation is necessary. The approach in this article to a case of Chenciner bifurcation is theoretical, but it can provide an answer for a number of applications of dynamical systems. We studied the bifurcation scenario and found out that, by this transformation, four different bifurcation diagrams are obtained, and the non-degenerate Chenciner bifurcation can be described by two bifurcation diagrams.

Dynamic Characteristics of Reinforced Concrete Beams Made of Carbonate Concrete

The ability of solid structures to absorb a certain part of the energy of dynamic impacts has not been properly reflected in impact theories. Meanwhile the effect of material properties on the various structures in the impact is so much that ignoring it when the solution of a large number dynamic problems makes it impossible to explain without distorting quantitatively and qualitatively, many of the actually observed phenomena, for example, equalization of dynamic stresses in places of their concentration and fluctuation of other parameters. In the article, two independent parameters for conventional reinforced concrete beams and those made of limestone concrete are compared, namely dynamic coefficient and the values of elastic rebound in impact. The effect of the reinforcement is not discussed in the paper.

Gravitational effect of plasma particles on the shadow of Schwarzschild black holes

Considering a Schwarzschild black hole surrounded by a fully ionized hydrogen plasma, we study the effect of the gravitational field of the plasma particles on the shadow. We take a formalism in which this effect is unified with the refractive effect of the plasma medium studied previously, but the two effects are characterized by two independent parameters. For semi-realistic values of parameters, we find their corrections to the shadow radius are both negligible, and the gravitational correction can overtake the refractive correction for active galactic nuclei of masses larger than $$10^9M_{\odot }$$ 10 9 M ⊙ . With unrealistically large values of parameters, we illustrate the two effects on the light trajectories and the intensity map.

Reengineering Cracker-Dryer Machine Based on Fan speed and Temperature Considering Drying Time, Final Weight and Energy Consumption Factor

Redesign and building a cracker drying machine should give priority to several factors to find the optimal point, one of which is by conducting experimental experiments. This research was carried out to find out from the tool and also pay attention to several things, such as temperature and fan speed. If one of these factors is ignored, it will not produce dry crackers and the dried crackers are less than optimal. The Independent parameters used in this research are temperature and fan speed. Dependent parameters used in this research are concerning drying time, final weight, and energy consumption. Design experiment using Factorial 3x3. Fan speed has 3 levels, they are 1000rpm, 1500rpm and 2000rpm. The Temperature parameter has 3 levels, they are 16, 19, and 21oC. Based on the design of experiment results, it was found that the drying time response for the combination that has the highest ranking is at a temperature of 19oC with a 2000rpm fan speed resulting in a drying time of 182,677 minutes.

Decoupling approximation of P- and S-wave phase velocities in orthorhombic media

Characterizing the kinematics of seismic waves in elastic orthorhombic media involves nine independent parameters. All wave modes, P-, S1-, and S2-waves, are intrinsically coupled. Since the P-wave propagation in orthorhombic media is weakly dependent on the three S-wave velocity parameters, they are set to zero under the acoustic assumption. The number of parameters required for the corresponding acoustic wave equation is thus reduced from nine to six, which is very practical for the inversion algorithm. However, the acoustic wavefields generated by the finite-difference scheme suffer from two types of S-wave artifacts, which may result in noticeable numerical dispersion and even instability issues. Avoiding such artifacts requires a class of spectral methods based on the low-rank decomposition. To implement a six-parameter pure P-wave approximation in orthorhombic media, we develop a novel phase velocity approximation approach from the perspective of decoupling P- and S-waves. In the exact P-wave phase velocity expression, we find that the two algebraic expressions related to the S1- and S2-wave phase velocities play a negligible role. After replacing these two algebraic expressions with the designed constant and variable respectively, the exact P-wave phase velocity expression is greatly simplified and naturally decoupled from the characteristic equation. Similarly, the number of required parameters is reduced from nine to six. We also derive an approximate S-wave phase velocity equation, which supports the coupled S1- and S2-waves and involves nine independent parameters. Error analyses based on several orthorhombic models confirm the reasonable and stable accuracy performance of the proposed phase velocity approximation. We further derive the approximate dispersion relations for the P-wave and the S-wave system in orthorhombic media. Numerical experiments demonstrate that the corresponding P- and S-wavefields are free of artifacts and exhibit good accuracy and stability.

Procedure for determining the constants of JH-2 (Johnson – Holmquist) dynamic fracture model for brittle materials

A simplified method for evaluating the constants in the JH-2 (Johnson – Holmqvist) model of the dynamic fracture for brittle materials is presented. The classical procedure suggests the use of 21 independent parameters describe the material, and the problem of their determination entails a large number of calculations experiments which hamper the use of the JH-2 model. The proposed technique requires fewer complex calculations and experimental data to determine the parameters of the material thus making it more feasible in use. In this work, the technique is used to search for the parameters of aluminum oxide (Al2O3) with a density of 99.5%, which is the material of a ceramic barrier subjected to high-speed interaction with the impactor. We present the results of three tests for penetration of a corundum plate: two of them are used to determine the constants of the model, and the third is used to verify the obtained values. Note that, the results obtained using the presented approach match quite accurately the experimental data, which is demonstrated in the course verification of the procedure.

Variety of fiber orientation tensors

Fiber orientation tensors are established descriptors of fiber orientation states in (thermo-)mechanical material models for fiber-reinforced composites. In this paper, the variety of fourth-order orientation tensors is analyzed and specified by parameterizations and admissible parameter ranges. The combination of parameterizations and admissible parameter ranges allows for studies on the mechanical response of different fiber architectures. Linear invariant decomposition with focus on index symmetry leads to a novel compact hierarchical parameterization, which highlights the central role of the isotropic state. Deviation from the isotropic state is given by a triclinic harmonic tensor with simplified structure in the orientation coordinate system, which is spanned by the second-order orientation tensor. Material symmetries reduce the number of independent parameters. The requirement of positive-semi-definiteness defines admissible ranges of independent parameters. Admissible parameter ranges for transversely isotropic and planar cases are given in a compact closed form and the orthotropic variety is visualized and discussed in detail. Sets of discrete unit vectors, leading to selected orientation states, are given.

A Real-Time Friction Prediction Model for in Service Drill String Based on Machine Learning Methods Coupling with Mechanical Mechanism Analysis

With highly deviated wells and horizontal wells are widely used in the oil industry. The large slope well sections and long horizontal well sections will lead to a sharp increase of the drill string torque and friction, which may reduce the drilling efficiency, and even lead to accidents. Therefore, real-time and accurate analysis of drill string’s torque and friction is an urgent problem facing by the modern drilling technology. The paper established a real-time friction prediction model that combines machine learning methods with drill string mechanical mechanism analysis model. Based on 84000 sets of field monitoring data obtained on-site, a regular data training set for weight on bit (WOB) and torque prediction was constructed with 23 types of time-series related parameters and 10 types of timing independent parameters. Relationships between time-series related parameters and timing independent parameters with the weight on bit and torque were trained to utilize long and short-term memory (LSTM) neural network and muti-layer back propagation (BP) network respectively. The new developed LSTM-BP neural network achieves high-precision prediction results of WOB and torque with a relative error of less than 14%. Based on derived WOB and torque prediction results, a theoretical mechanical analysis model of the entire drill string was adopted in this paper to develop the quantitative relation between WOB and torque with the friction coefficient of the drill string and oil casing. Suitable friction coefficients along the drill string can be finally obtained by solving the equilibrium function between predicted WOB, torque and measured hook load, rotary-table torque via an iteration algorithm. A case study was performed finally using the proposed intelligent analysis method to calculate the friction coefficients. This proposed methodology can be referenced to decrease the sticking risks and improve the drilling efficiency, which can finally increase the extension limit of horizontal wells in complex strata.